Question

已知a>0b>0 a+2√ab-15b=0,求(a-b)/(a+√ab)的值

Answer 1

a+2√ab-15b=0(√a)²+2√ab-15(√b)²=0(√a-3√b)(√a+5√b)=0√a-3√b=0或 √a+5√b=0（舍去）√a=3√ba=9b于是

(a-b)/(a+√ab)=(9b-b)/(9b+√9b·b)=8b/(9b+3b)=8/12=2/3