Question

已知a+b=-6,ab=8,化简求值：√(a/b)+√(b/a)

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

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