一道英文数学题If x,y and z are positive numbers such that x+y-5z=0

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一道英文数学题
If x,y and z are positive numbers such that x+y-5z=0 and x-y+z=0,then the value of x^2-y^2/z^2-x^2 is

x,y,z为正数,x+y-5z=0,x-y+z=0,求x^2-y^2/z^2-x^2 的值
x+y-5z=0
x-y+z=0
两式相减：y-3z=0 y=3z z=1/3y
代入1式：x-2z=0 x=2z x=2/3y y=3/2x
所以 y=3/2x z=1/2x
所求式=(x^2-9x^2/4) / x^2/4-x^2= (-5/4) / (-3/4)= 5/3

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