若a^2+b^2=3ab,求分式(1+2b^2/a^2-b^2)(1+2b/a-b)的值.

问题描述:

若a^2+b^2=3ab,求分式(1+2b^2/a^2-b^2)(1+2b/a-b)的值.

a^2+b^2=3ab
a^2-2ab+b^2=ab
(a-b)^2=ab
(1+2b^2/a^2-b^2)(1+2b/a-b)
=(a^2+b^2)/(a^2-b^2) x(a+b)/(a-b)
==(a^2+b^2)/(a+b)(a-b) x(a+b)/(a-b)
=(a^2+b^2)/(a-b)^2
=3ab/ab
=3