Question

已知m=x+y,n=x-y,试用m,n表示（x³+y³﹚²+（x³-y³

Answer 1

x＋y＝m

x－y＝n

∴ x＝﹙m＋n﹚/2

y＝﹙m－n﹚/2

x·y＝﹙m²－n²﹚/4

∴ ﹙x³＋y³﹚²＋﹙x³－y³﹚²

＝﹙x＋y﹚²﹙x²－xy＋y²﹚²＋﹙x－y﹚²﹚﹙x²＋xy＋y²﹚²

＝m²[﹙x－y﹚²＋xy]²＋n²[﹙x＋y﹚²－xy]²

＝m²﹙n²＋xy﹚²＋n²﹙m²－xy﹚²

＝m²·[﹙m²＋3n²﹚/4]²＋n²·[﹙3m²＋n²﹚/4]²