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已知(y+z-x)/(x+y+z)=(z+x-y)/(y+z-x)=(x+y-z)/(z+x-y)=p,求p^3+p^2+p的值
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已知(y+z-x)/(x+y+z)=(z+x-y)/(y+z-x)=(x+y-z)/(z+x-y)=p,求p^3+p^2+p的值
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答案和解析
那个?x+y+z不=0啊,做分母啊
p^3=(z+x-y)/(y+z-x) * (x+y-z)/(z+x-y) * (y+z-x)/(x+y+z)
= (x+y-z)/(x+y+z)
p^2 = (y+z-x)/(x+y+z) * (z+x-y)/(y+z-x)
= (z+x-y)/(z+x+y)
p = (y+z-x)/(x+y+Z)
p^3+p^2+p= (x+y-z+z+x-y+z-x+y)/(z+x+y)
= 1
p^3=(z+x-y)/(y+z-x) * (x+y-z)/(z+x-y) * (y+z-x)/(x+y+z)
= (x+y-z)/(x+y+z)
p^2 = (y+z-x)/(x+y+z) * (z+x-y)/(y+z-x)
= (z+x-y)/(z+x+y)
p = (y+z-x)/(x+y+Z)
p^3+p^2+p= (x+y-z+z+x-y+z-x+y)/(z+x+y)
= 1
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