Question

若a>b>0,a的平方+b的平方-6ab=0,则b-a分之a+b的值为多少?

Answer 1

a^2+b^2-6ab=0

a^2+b^2=6ab

a^2+b^2+2ab=8ab a^2+b^2-2ab=4ab

(a+b)^2=8ab (a-b)^2=4ab

a+b=2√(2ab) a-b=2√(ab)

(a+b)/(b-a)

=2√(2ab)/(-2√ab)

=-√2