2x+3y+z=13 4x^2+9y^2+z^2-2x+15y+3z=82 求x,y,z
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2x+3y+z=13 4x^2+9y^2+z^2-2x+15y+3z=82 求x,y,z
x=3,y=1,z=4
2x+3y+z=13 (1) 4x^2+9y^2+z^2-2x+15y+3z=82 (2)
11 (1)* (2) ------》4x^2+9y^2+z^2-24x-18y-8z+61=0
配方-----》4(x-3)^2+9(y-1)^2+(z-4)^2=0
-----》x=3,y=1,z=4
再问: 11 (1)* (2) ------》4x^2+9y^2+z^2-24x-18y-8z+61=0 是怎么的出来的?
再答: (2)-11(1)
2x+3y+z=13 (1) 4x^2+9y^2+z^2-2x+15y+3z=82 (2)
11 (1)* (2) ------》4x^2+9y^2+z^2-24x-18y-8z+61=0
配方-----》4(x-3)^2+9(y-1)^2+(z-4)^2=0
-----》x=3,y=1,z=4
再问: 11 (1)* (2) ------》4x^2+9y^2+z^2-24x-18y-8z+61=0 是怎么的出来的?
再答: (2)-11(1)
试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y)
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