TIInterActive FileМЉTrediegradsligninger Generelle lјsningsformler for trediegradsligninger er ikke pensum pх gymnasialt niveau, men de kan klares med nogle snedige variabelskift (substitutioner), hvorved ligningen цndrer form, og det til sidst lykkes at komme igennem til en lјsningsformel. Den specielle trediegradsligning  som ikke indeholder noget andengradsled, kan lјses med Cardanos formel, som udledes nedenfor. Fјrst erstattes y med formlen u + v, sх vi nu fхr to ubekendte, u og v:  Med lidt faktorisering i midten fхr vi fјlgende omskrivning  Vi fхr ligningen ovenfor opfyldt, hvis vi fхr nedenstхende to ligninger opfyldt:   hvoraf  Nu kender vi хbenbart sum og produkt af stјrrelserne u3 og v3, som derfor ifјlge sцtning om sum og produkt af rјdderne i den reducerede andengradsligning mх vцre lјsninger til   Hvis p3 + q2 > 0 kan vi lјse sхdan:       Den generelle trediegradsligning  kan omformes til formen ovenfor (uden andengradsled) ved hjцlp af en lineцr substitution x=y+c  Her bortfalder andengradsleddet, hvis vi vцlger c, sх 3ac + b = 0   som er den specielle trediegradsligning, hvor  og  Eksempel: Ligningen  har  og  og har efter Cardanos formel fјlgende lјsning:  Her er TI Interactive ikke overbevisende til at reducere udtryk med rјdder, men efter indstilling til at regne tilnцrmet (Mode Settings: Computation: Approximate) fхs  som ved direkte indsцttelse ses at stemme eksakt. ^˜3PP§P P3:PmP|8PД<PЕPК<PЛ~P9<P:P><P?#Pb#P…ъPoPw3PpўМTimes New RomanџМTimes New RomanџTimes New RomanшўМTimes New Roman8џTimes New Roman3456лмноlmno}~./0123VWXY[\]^_`abde…†‡ˆцчшщ456789fglmnoxy‚ƒŠ‹‘’“”ТУФХklno ЁЁЂЄЅЅІІЇЇЈЈЉЉЊЊ€d а p@ рА€P №Р!$`'d а p@ рА€P №Р!$`'€ Š@dd w;474џџ CTxobjItem4аЯрЁБс>ўџ ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ§џџџўџџџ 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TŸўpFАўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџNANIHўџџwўџџ˜ўџџ€  @dd7w;272џџ CTxobjItem2аЯрЁБс>ўџ 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0 190 1000001Џџџџџџџ€ ”J@dd" w;F7Fџџ CTxobjItem$FаЯрЁБс>ўџ  ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ§џџџўџџџ ўџџџџџџџџџџџџџџџџџџџџџџџўџџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџRoot 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0 10000300 1e80 8f00 7100 0 ffff00 1000000 0 20000000 448010 8f0000 710000 0 ffff0000 0 1 0 1e80102b 8f000000 71000000 0 ff000000 ff 100 0 2000 0 0 0 80150000 35 8f 71 0 ffff 10000 0 10000 35800b 8f0000 710000 0 ffff0000 0 1 0 80100001 35 8f 71 0 10003 10000 0 630000 0 0 1400 19000000 1780 9600 7800 0 1ffff00 1000000 0 1000000 17800b00 96000000 78000000 0 ff000000 ff 100 0 1c000100 1780 9600 7800 0 100 1000000 0 d7000000 0 0 0 0 3c8015 8f0000 710000 0 ffff0000 0 1 0 800b0001 3c 8f 71 0 ffff 10000 0 10000 3c8010 8f0000 710000 0 30000 1 1 0 78 0 14000000 0 80801900 8f000000 71000000 0 ff000000 1ff 100 0 b000100 8080 8f00 7100 0 ffff00 1000000 0 3000000 1e801000 8f000000 71000000 0 ff000000 ff 100 0 80102000 44 8f 71 0 ffff 10000 0 102b0000 1e80 8f00 7100 0 ffff00 1000000 0 20000000 0 0 0 0 3c8015 8f0000 710000 0 ffff0000 0 1 0 800b0001 3c 8f 71 0 ffff 10000 0 10000 3c8010 8f0000 710000 0 30000 1 1 0 64 0 14000000 0 1ffff00 43000f00 70796c47 544f4d68 6d6d6972 806465 8f0000 710000 0 ffff0000 1 1 0 800b0001 80 8f 71 0 ffff 10000 0 30000 1e8010 8f0000 710000 0 ffff0000 0 1 0 44801020 8f000000 71000000 0 ff000000 ff 100 0 80103d00 1e 8f 71 0 ffff 10000 0 200000 0 0 0 34000000 3c80 8f00 7100 0 ffff00 1000000 0 1000000 3c800b00 8f000000 71000000 0 ff000000 ff 100 0 10000100 3c80 8f00 7100 0 1ffff00 1000000 0 30000000 0 0 140000 0 1802a 8f0000 ffff0000 ffff ffff0000 1 1 0 0 0 140000 25 25 25 25 0 5cf ed ffffffff ffffffff 1ffff 10000 0 0 0 10000 0 30000 43050000 5453454d 80000002 1203d02 0(33 10001 0 0 0 0 13601 0 10000 0 0 0 0 0d@@'eq := a*(x)^(3) + b*(x)^(2) + c*x + d=0Times New Roman џџџџ!a*(x)^(3) + b*(x)^(2) + c*x + d=0Times New Roman џџџџ=  80340002 2d 69 53 0 ffff 10000 0 10000 2d800b 690000 530000 0 ffff0000 0 1 0 80100001 2d 69 53 0 1ffff 10000 0 330000 0 0 1400 2a000000 180 6900 ffffff00 ff 1ffff00 1000000 0 0 0 0 2c001400 80 0 0 0 1000100 0 0 29000000 802a 0 0 0 ffff0000 1 0 0 0 0 140000 0 8b0084 85 0 808019 8f0000 710000 0 ffff0000 1 1 0 800b0001 80 8f 71 0 ffff 10000 0 30000 1e8010 8f0000 710000 0 ffff0000 0 1 0 44801020 8f000000 71000000 0 ff000000 ff 100 0 80102b00 1e 8f 71 0 ffff 10000 0 200000 0 0 0 34000000 3c80 8f00 7100 0 ffff00 1000000 0 1000000 3c800b00 8f000000 71000000 0 ff000000 ff 100 0 10000100 3c80 8f00 7100 0 1ffff00 1000000 0 34000000 0 0 140000 0 178019 960000 780000 0 ffff0000 1 1 0 800b0001 17 96 78 0 ffff 10000 0 10000 17801c 960000 780000 0 10000 0 1 0 d7 0 0 0 6b801e00 b1000000 93000000 0 ff000000 1ff 100 0 20000200 3d80 8f00 7100 0 ffff00 1000000 0 1000000 800b00 0 0 0 ff000000 ff 100 0 23000400 80 0 0 0 1000100 0 0 28000000 3d8009 8f0000 710000 0 ffff0000 0 1 0 800b0001 3d 8f 71 0 ffff 10000 0 20000 3c8015 8f0000 710000 0 ffff0000 0 1 0 800b0001 3c 8f 71 0 ffff 10000 0 10000 3c8010 8f0000 710000 0 30000 1 1 0 71 0 14000000 0 1802a00 8f000000 ff000000 ffffff ff000000 1ff 100 0 0 0 14000000 802c00 0 0 0 1000000 100 0 0 802a2900 0 0 0 0 1ffff 0 0 0 0 0 14 9b0000 9c00a2 2e8020 690000 530000 0 ffff0000 0 1 0 800b0001 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3d028000 120 0(33 10001 0 0 0 0 13601 0 10000 0 0 0 0 0d@@'eq := a*(x)^(3) + b*(x)^(2) + c*x + d=0Times New Roman џџџџ5a*(x)^(3) + b*(x)^(2) + c*x + 4*(p)^(3) + 4*(q)^(2)=0Times New Roman џџџџ= ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџNANIЏ3џџџmLџџџ€ kM@ddС я;L7Lџџ CTxobjItem'LаЯрЁБс>ўџ #ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ§џџџўџџџ  !"ўџџџўџџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџRoot Entryџџџџџџџџ‚ђZnЪв–@3ЅађqёœЫФ$@ContentsџџџџџџџџџџџџзAOlePres000џџџџџџџџџџџџџџџџџџџџЦ9iџн 86e 64 64 1 1 1 0 ffff0007 b0002 796c4743 74536870 88656c79 ffffff 0 0 90000000 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ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ§џџџўџџџ ўџџџўџџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџRoot Entryџџџџџџџџ‚ђZnЪв–@3ЅађqёœЫФ@ContentsџџџџџџџџџџџџМOlePres000џџџџџџџџџџџџџџџџџџџџ\`џ‚c98 64 64 1 1 1 0 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1000000(33 10001 0 0 0 0 13601 0 10000 0 0 0 0 0d@@?2*q= (d)/(a) - (b*c)/(3*(a)^(2)) + (2*(b)^(3))/(27*(a)^(3))Times New Roman џџџџ?2*q= (d)/(a) - (b*c)/(3*(a)^(2)) + (2*(b)^(3))/(27*(a)^(3))Times New Roman џџџџ= ьŸ\Л (b 0  ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџNANIЏbM—€ јa@ddыw;.7.џџ CTxobjItem3.аЯрЁБс>ўџ 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ffff00 1000000 0 1000000 2d801000 69000000 53000000 0 ff000000 1ff 100 0 3300 0 0 14 ffff0000 a0001 796c4743 65546870 16d72 690000 ffff0000 ffff ffff0000 1 1 0 0 0 140000 1ffff 47430010 6870796c 65726150 6769526e 7468 0 0 0 10000 1 0 0 802229 0 0 0 ff000000 1ff 0 0 0 0 14000000 0 25001b00 ff001c00 b0001ff 6c474300 4d687079 54525153 187 cb ad 0 ffff 10000 0 10000 141800b ad0000 8f0000 0 ffff0000 0 1 0 80090002 140 ad 8f 0 ffff 10000 0 10000 140800b ad0000 8f0000 0 ffff0000 0 1 0 80270004 83 ad 8f 0 1ffff 10000 0 10000 3d800b 8f0000 710000 0 ffff0000 0 1 0 801e0002 3c 8f 71 0 ffff 10000 0 10000 3c800b 8f0000 710000 0 ffff0000 0 1 0 80100001 3c 8f 71 0 1ffff 10000 0 350000 0 0 1400 22000000 180 8f00 ffffff00 ff 1ffff00 1000000 0 0 0 0 ff001400 80001ff 6c474300 4d687079 804f 8f00 7100 0 1ffff00 1000000 0 1000000 80800b00 8f000000 71000000 0 ff000000 ff 100 0 10000300 1e80 8f00 7100 0 ffff00 1000000 0 20000000 448010 8f0000 710000 0 ffff0000 0 1 0 1e80102b 8f000000 71000000 0 ff000000 ff 100 0 2000 0 0 0 801e0000 3c 8f 71 0 ffff 10000 0 10000 3c800b 8f0000 710000 0 ffff0000 0 1 0 80100001 3c 8f 71 0 1ffff 10000 0 320000 0 0 1400 22000000 180 ad00 ffffff00 ff 1ffff00 1000000 0 0 0 0 22001400 180 ad00 ffffff00 ff 1ffff00 1000000 0 0 0 0 1400 0 69803200 8f000000 71000000 0 ff000000 1ff 100 0 b000100 6980 8f00 7100 0 ffff00 1000000 0 3000000 1e801000 8f000000 71000000 0 ff000000 ff 100 0 80102000 2d 8f 71 0 ffff 10000 0 102d0000 1e80 8f00 7100 0 ffff00 1000000 0 20000000 0 0 0 0 18e8015 cb0000 ad0000 0 ffff0000 1 1 0 80170002 2e 69 53 0 ffff 10000 0 10000 800b 0 0 0 ffff0000 0 1 0 801a0004 0 0 0 0 10001 0 0 9280000 2e80 6900 5300 0 ffff00 1000000 0 1000000 2e800b00 69000000 53000000 0 ff000000 ff 100 0 1e000200 2d80 6900 5300 0 ffff00 1000000 0 1000000 2d800b00 69000000 53000000 0 ff000000 ff 100 0 10000100 2d80 6900 5300 0 1ffff00 1000000 0 33000000 0 0 140000 0 18022 690000 ffff0000 ffff ffff0000 1 1 0 0 0 140000 8024 0 0 0 10000 1 0 0 802229 0 0 0 ff000000 1ff 0 0 0 0 14000000 0 4c004500 27004600 17080 cb00 ad00 0 ffff00 1000000 0 1000000 2a800b00 ad000001 8f000000 0 ff000000 ff 100 0 9000200 12980 ad00 8f00 0 ffff00 1000000 0 1000000 29800b00 ad000001 8f000000 0 ff000000 ff 100 0 27000400 8380 ad00 8f00 0 1ffff00 1000000 0 1000000 3d800b00 8f000000 71000000 0 ff000000 ff 100 0 1e000200 3c80 8f00 7100 0 ffff00 1000000 0 1000000 3c800b00 8f000000 71000000 0 ff000000 ff 100 0 10000100 3c80 8f00 7100 0 1ffff00 1000000 0 35000000 0 0 140000 0 18022 8f0000 ffff0000 ffff ffff0000 1 1 0 0 0 140000 698032 8f0000 710000 0 ffff0000 1 1 0 800b0001 69 8f 71 0 ffff 10000 0 30000 1e8010 8f0000 710000 0 ffff0000 0 1 0 2d801020 8f000000 71000000 0 ff000000 ff 100 0 80102d00 1e 8f 71 0 ffff 10000 0 200000 0 0 0 1e000000 3c80 8f00 7100 0 ffff00 1000000 0 1000000 3c800b00 8f000000 71000000 0 ff000000 ff 100 0 10000100 3c80 8f00 7100 0 1ffff00 1000000 0 32000000 0 0 140000 0 18022 ad0000 ffff0000 ffff ffff0000 1 1 0 0 0 140000 18022 ad0000 ffff0000 ffff ffff0000 1 1 0 0 0 140000 0 80220000 1 cb ffffffff 0 1ffff 10000 0 0 0 0 1d0014 1d0000 1d0000 1d0000 0 4ef0000 1070000 ffff0000 ffffffff ffffffff 1 1 0 0 0 1 0 3 454d4305 25453 3d028000 120 0(33 10001 0 1 1 0 13601 0 10000 0 0 0 0 0d@@gy := ( sqrt((p)^(3) + (q)^(2)) - q)^(1/(3)) - ( sqrt((p)^(3) + (q)^(2)) + q)^(1/(3)) | p=1 and q=-2Times New Roman џџџџ1( sqrt(5) + 2)^(1/(3)) - ( sqrt(5) - 2)^(1/(3))Times New Roman џџџџ= = 00 710000 0 ffff0000 1 1 0 800b0001 80 8f 71 0 ffff 10000 0 30000 1e8010 8f0000 710000 0 ffff0000 0 1 0 44801020 8f000000 71000000 0 ff000000 ff 100 0 80102b00 1e 8f 71 0 ffff 10000 0 200000 0 0 0 2e000000 6b80 b100 9300 0 1ffff00 1000000 0 2000000 3d801700 8f000000 71000000 0 ff000000 ff 100 0 b000100 80 0 0 0 ffff00 1000000 0 4000000 801a00 0 0 0 1000000 100 0 0 80092800 3d 8f 71 0 ffff 10000 0 10000 3d800b 8f0000 710000 0 ffff0000 0 1 0 80350002 3c 8f 71 0 ffff 10000 0 10000 3c800b 8f0000 710000 0 ffff0000 0 1 0 80100001 3c 8f 71 0 10003 10000 0 710000 0 0 1400 22000000 180 8f00 ffffff00 ff 1ffff00 1000000 0 0 0 0 24001400 80 0 0 0 1000100 0 0 29000000 8022 0 0 0 ffff0000 1 0 0 0 0 140000 0 ac00a5 801700a6 2e 69 53 0 ffff 10000 0 10000 800b 0 0 0 ffff0000 0 1 0 801a0004 0 0 0 0 10001 0 0 9280000 2e80 6900 5300 0 ffff00 1000000 0 1000000 2e800b00 69000000 53000000 0 ff000000 ff 100 0 1e000200 2d80 6900 5300 0 ffff00 1000000 0 1000000 2d800b00 69000000 53000000 0 ff000000 ff 100 0 10000100 2d80 6900 5300 0 1ffff00 1000000 0 32000000 0 0 140000 0 18022 690000 ffff0000 ffff ffff0000 1 1 0 0 0 140000 8024 0 0 0 10000 1 0 0 802229 0 0 0 ff000000 1ff 0 0 0 0 14000000 0 b700b000 b100 0 1802200 b1000000 ff000000 ffffff ff000000 1ff 100 0 0 0 14000000 80804700 8f000000 71000000 0 ff000000 1ff 100 0 b000100 8080 8f00 7100 0 ffff00 1000000 0 3000000 1e801000 8f000000 71000000 0 ff000000 ff 100 0 80102000 44 8f 71 0 ffff 10000 0 102b0000 1e80 8f00 7100 0 ffff00 1000000 0 20000000 0 0 0 0 3c8035 8f0000 710000 0 ffff0000 0 1 0 800b0001 3c 8f 71 0 ffff 10000 0 10000 3c8010 8f0000 710000 0 30000 1 1 0 71 0 14000000 0 1802200 cf000000 ff000000 ffffff ff000000 1ff 100 0 0 0 14000000 1802200 cf000000 ff000000 ffffff ff000000 1ff 100 0 0 0 14000000 0 22000000 180 ed00 ffffff00 ff 1ffff00 1000000 0 0 0 0 49001400 49000000 49000000 49000000 0 41000000 29000007 ff000001 ffffffff ffffffff 1ff 100 0 0 0 100 0 300 4d430500 2545345 2800000 1203d ff0000(33 10001 0 0 0 0 13601 0 10000 0 0 0 0 0d@@Wy := ( sqrt((p)^(3) + (q)^(2)) - q)^(1/(3)) - ( sqrt((p)^(3) + (q)^(2)) + q)^(1/(3))Times New Roman џџџџQ( sqrt((p)^(3) + (q)^(2)) - q)^(1/(3)) - ( sqrt((p)^(3) + (q)^(2)) + q)^(1/(3))Times New Roman џџџџ= ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџNANIЏ4ЕX€ 7m@ddйя;N7Nџџ CTxobjItem@NаЯрЁБс>ўџ #ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ§џџџўџџџ ўџџџ !"%ўџџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџRoot Entryџџџџџџџџ‚ђZnЪв–@3ЅаIП BЬФ$РContentsџџџџџџџџџџџџ<4OlePres000џџџџџџџџ”џџџџџџџџџџџџ*iџ+23e0 64 64 1 1 1 0 ffff0007 b0002 796c4743 74536870 b1656c79 ffffff 0 0 90000000 1 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