Question

设a,b为非零实数,且a^2+b^2=4ab.求(a+b/a-b)^2的值

计算:(a^2-b^2/a^3+b^3)/(a^2-2ab+b^2/a^2-ab+b^2)*1/(b-a)^2

Answer 1

1.设a,b为非零实数,且a²+b²=4ab.求[(a+b)/(a-b)]²的值
解：a²-2ab+b²=2ab，故(a-b)²=2ab
∴[(a+b)/(a-b)]²=(a+b)²/(a-b)²=(a²+2ab+b²)/2ab=(6ab)/2ab=3
2.计算:[(a²-b²)/(a³+b³)]/[(a²-2ab+b²)/(a²-ab+b²)][1/(b-a)²]
原式=[(a²-b²)/(a³+b³)][(a²-ab+b²)/(a-b)²][1/(a-b)²]
=[(a-b)/(a²-ab+b²)][(a²-ab+b²)/(a-b)²][1/(a-b)²]
=[1/(a-b)][1/(a-b)²]=1/(a-b)³

Answer 2

解答：由条件式配方得：①﹙a＋b﹚²=6ab，②﹙a－b﹚²=2ab，代入[﹙a＋b﹚／﹙a－b﹚]²=﹙6ab﹚／﹙2ab﹚=3。补充问题的方法相同。

Answer 3

fsf