已知 a+b=-4√2,ab=8.求√a/b+√b/a的值

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已知a+b=-4√2,ab=8.求√a/b+√b/a的值已知a+b=-4√2,ab=8.求√a/b+√b/a的值已知a+b=-4√2,ab=8.求√a/b+√b/a的值a,b是x^2+(+4√2)*x

已知 a+b=-4√2,ab=8.求√a/b+√b/a的值
已知 a+b=-4√2,ab=8.求√a/b+√b/a的值

已知 a+b=-4√2,ab=8.求√a/b+√b/a的值
a, b 是 x^2 + (+4√2) * x + 8 = 0 的两个根,可求出:
x1 = x2 = -2√2
于是 a = b = = -2√2
√a/b + √b/a = -1/√2

√a/b+√b/a
=√a/√b+√b/√a
=√(ab)/b+√(ab)/a
=a√(ab)/(ab)+b√(ab)/ab
=(a+b)/√(ab)
=-√2/2