Question

①已知1/x-1/y=3,求5x+xy-5y/x-xy-y的值.

Answer 1

∵1/x-1/y=3

∴y-x=3xy

(5x+xy-5y)/(x-xy-y)=(5x-5y+xy)/(x-y-xy)=(-15xy+xy)/(-3xy-xy)=3.5

∵m²+n²=4mn

∴m²+n²-2mn=2mn

∴(m-n)²=2mn

又∵m＞n＞0

∴m-n=√(2mn)

∵m²+n²=4mn

∴m²+n²+2mn=6mn

∴(m+n)²=6mn

又∵m＞n＞0

∴m+n=√(6mn)

∴(m²-n²)/mn=(m+n)(m-n)/mn=2√3

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