Question

若(a2+1)(b2+1)=4ab,则a2-3a+1=?

Answer 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