已知a、b是方程x的平方减7x加9等于0的两根,且a小于b,则根号a加根号b分之根号a减根号b的值为多少?

a、b是方程x^2-7x+9=0
则a+b=7,ab=9
(a-b)^2 = (a+b)^2-4ab = 7^2-4*9 = 13
a＜b
a-b = -√13
(√a-√b)/(√a+√b)
= (√a-√b)^2/(a-b)
= {(a+b-2√(ab)}/(a-b)
= {7-2√9)}/(-√13)
=（7-6)√13/(-13)
= -√13/13