已知X分之1+Y分之1=5,求X+2XY+Y分之2X-5XY+2Y的值

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已知X分之1+Y分之1=5,求X+2XY+Y分之2X-5XY+2Y的值

已知X分之1+Y分之1=5,求X+2XY+Y分之2X-5XY+2Y的值
已知X分之1+Y分之1=5,求X+2XY+Y分之2X-5XY+2Y的值

已知X分之1+Y分之1=5,求X+2XY+Y分之2X-5XY+2Y的值
∵1/x+1/y=5
∴(x+y)/(x*y)=5
∴x+y=5xy
所以(2x-5xy+2y)/(x+2xy+y)=(10xy-5xy)/(5xy+2xy)=5/7

给X分之1+Y分之1=5同乘xy,则x+y=5xy,带入X+2XY+Y分之2X-5XY+2Y等于7XY/5xy=7/5

(2X-5XY+2Y)/(X+2XY+Y)=(2(X+Y+2XY)-9XY)/(X+2XY+Y)=2-9XY/(X+2XY+Y)
上下都除以XY得
2-9/(1/Y+1/X+2)=2-9/(5+2)=-5/7