诺(a²+1)(b²+1)=4ab,求a²-3b+1

问题描述:

诺(a²+1)(b²+1)=4ab,求a²-3b+1

(a²+1)(b²+1)=4ab
a²b²-2ab+1+a²+b²-2ab=0
(ab-1)²+(a-b)²=0两个非负数的和等于0
所以,ab-1=0,a-b=0
ab=1,a=b=1或-1
a²-3b+1=3或-3