已知2x-3y-z=0.x+3y-14z=0,x,y,z不全为0.求xy+yz+xz分之4x的平方-(5xy+z)的平方

问题描述:

已知2x-3y-z=0.x+3y-14z=0,x,y,z不全为0.求xy+yz+xz分之4x的平方-(5xy+z)的平方

(4x)平方-(5xy+z)平方
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xy+yz+xz

2x-3y-z=0 (1) x+3y-14z=0 (2) (1)+(2) 3x-15z=0 x=5z (2)*2-(1) 6y-28z+3y+z=0 9y=27z y=3z 代入 (4x^2-5xy+z^2)/(xy+yz+xz) =(100z^2-75z^2+z^2)/(15z^2+3z^2+5z^2) =26z^2/23z^2 =26/23