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已知4x-5y+2z=0,x+4y-3z=0,求(x²+y²+z²)/xy+yz+xz
人气:457 ℃ 时间:2019-12-10 02:55:56
解答
由4x-5y+2z=0,(1)
x+4y-3z=0,(2)
将2式乘以4减去1式,可以得出,21y=14z,即z=1.5y
代回1式可得,4x-5y+3y=0,即4x=2y,x=0.5y
分别代入(x²+y²+z²)/xy+yz+xz中,
即(0.25y²+y²+2.25y²)/(0.5y²+1.5y²+0.75y²)=14/11=1.273
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