Question

证明无论A,B取何值时,A的平方乘B的平方-2AB+2均为正值

Answer 1

a^2b^2-2ab+2=(ab)^2-2ab+1+1=(ab-1)^2+1

(ab-1)^2>=0

(ab-1)^2+1>0

a^2b^2-2ab+2>0