已知实数x、y、z,满足3x-2y-4z=-9且x+2y-4z=5,试求出x^2+y^2+z^2的最小值
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已知实数x、y、z,满足3x-2y-4z=-9且x+2y-4z=5,试求出x^2+y^2+z^2的最小值
已知实数x、y、z,满足3x-2y-4z=-9且x+2y-4z=5,试求出x^2+y^2+z^2的最小值
已知实数x、y、z,满足3x-2y-4z=-9且x+2y-4z=5,试求出x^2+y^2+z^2的最小值
3x-2y-4z=-9
x+2y-4z=5
联立方程解得:
y=0.5x+3.5
z=0.5x+0.5
所以有:
x²+y²+z²
=x²+(0.5x+3.5)²+(0.5x+0.5)²
=1.5x²+4x+12.5
=1.5[x²+8x/3+(4/3)²]-8/3+12.5
=1.5(x+4/3)²+59/6
所以可得:当x=-4/3 时有最小值为:59/6
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