Question

已知a>b>0,且a^2+b^2=3ab,求a^2+2ab+b^2/a-2b除以a^2-b^2/a-2b的值

Answer 1

∵a^2+b^2=3ab

∴a²+2ab+b²=5ab,a²-2ab+b²=ab

(a+b)²=5ab, (a-b)²=ab

a+b=√(5ab), a-b=√(ab) (∵a>b>0)

a^2+2ab+b^2/a-2b除以a^2-b^2/a-2b

=(a+b)²/[(a+b)(a-b)]

=(a+b)/(a-b)

=√(5ab)/√(ab)

=√5

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