已知a大于0b大于0且a-5根号ab+6b=0求根号a-根号b比上根号a+根号b的值

Question

已知a大于0 b大于0
且a-5根号ab+6b=0求根号a-根号b比上根号a+根号b 的值

Answer 1

因为a > 0 ,b > 0 a - 5√(ab) + 6b = 0
即有:(√a)^2 -5*√a*√b + 6(√b)^2 = 0
(√a -2√b)(√a - 3√b) = 0
所以有:√a = 2√b 或 √a = 3√b
(1) 当√a = 2√b时,(√a -√b)/(√a +√b) = (2√b -√b)/(2√b + √b) = √b/(3√b) = 1/3
(2) 当√a = 3√b时,(√a - √b)/(√a +√b) = (3√b -√b)/(3√b +√b ) = 2√b / 4√b = 1/2