Question

已知a+b=-6，ab=8试求√b/a+√a/b的值

Answer 1

∵√(a/b)+√(b/a)＞0 ∴√(a/b)+√(b/a) =√[√(a/b)+√(b/a)]² =√(a/b+b/a+2) =√[(a²+b²)/ab+2] =√[((a+b)²-2ab)/ab+2] =√[(-6)²-8×2)/8+2 =√(20/8+2) =√(9/2) =3√2/2