问题补充:
已知实数a>b>0,若满足a的平方+b的平方=3ab.则分式 a+b/a-b的值等于
答案:
∵a²+b²=3ab ,(a+b)²=a²+2ab+b²,(a-b)²=a²+b²-2ab
∴,(a+b)²=5ab,(a-b)²=ab
∵a>b>0∴a+b>0,a-b>0∴a+b=√5ab,a-b=√ab
于是a+b/a-b=√5ab/√ab=√5
======以下答案可供参考======
供参考答案1:
(a+b)²/(a-b)²
=(a²+2ab+b²)/(a²-2ab+b²)
=(3ab+2ab)/(3ab-2ab)
=5又a>b>0
开方得a+b/a-b=√5