a2b2+a2+b2+1=4ab 求a、b的值

a2b2+a2+b2+1=4ab 求a、b的值
a2b2+a2+b2+1=4ab 求a、b的值

a2b2+a2+b2+1=4ab 求a、b的值
a2b2+a2+b2+1=4ab
变形得：a^2b^2-2ab+1+a^2-2ab+b^2=0
(ab-1)^2+(a-b)^2=0
ab-1=0,a-b=0
得：a1=b1=1,或 a2=b2=1

a2b2+a2+b2+1=4ab =>(a2b2-2ab+1)+(a2-2ab+b2)=0 =>(a2b2-2ab+1)=0 (a2-2ab+b2)=0 =>ab-1=0 a=b => a=b=正负1

∵a2b2+a2+b2+1=4ab ，∴(a2b2-2ab+1）+（a2+b2-2ab)=0.∴(ab-1)2+(a-b)2=0.∴ab=1,a-b=0.∴a=b.∴a2=1,b2=1.∴a=±1,b=±1.