已知x^2+y^2+z^2≤2x+4y-6z-14,求x^2+y^2+z^2的值

2025-01-02 16:04:01
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回答1:

x^2+y^2+z^2≤2x+4y-6z-14
x^2-2x+1+y^2-4y+4+z^2+6z+9≤0
(x-1)^2+(y-4)^2+(z+3)^2≤0
所以有:x-1=0 得x=1
y-4=0 得:y=4
z+3=0 得:z=-3
x^2+y^2+z^2=1+16+9=26