若(a2+1)(b2+1)=4ab,则a2-3a+1=?

2025-02-27 07:42:29
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回答1:

a^2b^2+a^2+b^2+1=4ab
((ab)^2-2ab+1)+(a^2-2ab+b^2)=0
(ab-1)^2+(a-b)^2=0
therefore,
ab-1=0 and a-b=0
ab=1 and a=b
a=b=1 or a=b=-1

When a=1, a^2-3a+1=-1
when a=-1, a^2-3a+1=5