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
2x+3y+z=13 4x^2+9y^2+z^2-2x+15y+3z=82 求x,y,z

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