Question

已知:a*a*b*b+a*a+b*b+16=10ab.求a*a+b*的值.

Answer 1

a^2b^2+a^2+b^2+16=10ab

a^2b^2+a^2+b^2+16-10ab=0

(a^2+b^2-2ab)+(a^2b^2-8ab+16)=0

(a-b)^2+(ab-4)^2=0

因为(a-b)^2≥0,(ab-4)^2≥0,(a-b)^2+(ab-4)^2=0

所以(a-b)^2=0,(ab-4)^2=0

a-b=0,ab-4=0

所以a=b=2或a=b=-2

a^2+b^2=8