Question

已知4a^2+4ab+b^2=0,求a/b-b/a-(a^2+b^2)/ab的值

Answer 1

4a^2+4ab+b^2=0

(2a+b)^2=0

2a+b=0

b=-2a

a/b-b/a-(a^2+b^2)/ab

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

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

=[(a^2-b^2)-(a^2+b^2)]/ab

=(a^2-b^2-a^2-b^2)/ab

=(-2b^2)/ab

=-2b/a

=-2*(-2a)/a

=4a/a

=4