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已知实数xyz满足：(根号下x+2y-2z)+|2x-y-1z/4|=0,且xyz不是零求(2x+y-z)/(3x-2y+z)
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已知实数xyz满足：(根号下x+2y-2z)+|2x-y-1z/4|=0,且xyz不是零求(2x+y-z)/(3x-2y+z)
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答案和解析
√(x+2y-2z)+|2x-y-1/4z|=0
x+2y-2z=0
x+2y=2z.(1)
2x-y-1/4z=0
8x-4y-z=0
8x-4y=z.(2)
(1)*2+(2)：
2x+8x=4z+z
x=z/2
代入(1)：
z/2+2y=2z
2y=3/2z
y=3/4z
(2x+y-z)/(3x-2y+z)
=[2(z/2)+3/4z-z]/[3(z/2)-2(3/4z)+z]
=(z+3/4z-z)/(3/2z-3/2z+z)
=(3/4z)/z
=3/4
x+2y-2z=0
x+2y=2z.(1)
2x-y-1/4z=0
8x-4y-z=0
8x-4y=z.(2)
(1)*2+(2)：
2x+8x=4z+z
x=z/2
代入(1)：
z/2+2y=2z
2y=3/2z
y=3/4z
(2x+y-z)/(3x-2y+z)
=[2(z/2)+3/4z-z]/[3(z/2)-2(3/4z)+z]
=(z+3/4z-z)/(3/2z-3/2z+z)
=(3/4z)/z
=3/4
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