x,y为何值时,多项式4x²+9y²-4x+12y-1有最小值,并求出最小值?4x²+9y²-4x+12y-1=(4x²-4x+1)+(9y²+12y+4)-6=(2x-1)²+(3y+2)²-6由于(2x-1)²、(3y+2)²≥0,所以原多项式的最小值当(2x-1)&
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![x,y为何值时,多项式4x²+9y²-4x+12y-1有最小值,并求出最小值?4x²+9y²-4x+12y-1=(4x²-4x+1)+(9y²+12y+4)-6=(2x-1)²+(3y+2)²-6由于(2x-1)²、(3y+2)²≥0,所以原多项式的最小值当(2x-1)&](/uploads/image/z/1825546-58-6.jpg?t=x%2Cy%E4%B8%BA%E4%BD%95%E5%80%BC%E6%97%B6%2C%E5%A4%9A%E9%A1%B9%E5%BC%8F4x%26%23178%3B%2B9y%26%23178%3B-4x%2B12y-1%E6%9C%89%E6%9C%80%E5%B0%8F%E5%80%BC%2C%E5%B9%B6%E6%B1%82%E5%87%BA%E6%9C%80%E5%B0%8F%E5%80%BC%3F4x%26%23178%3B%2B9y%26%23178%3B-4x%2B12y-1%3D%284x%26%23178%3B-4x%2B1%29%2B%289y%26%23178%3B%2B12y%2B4%29-6%3D%282x-1%29%26%23178%3B%2B%283y%2B2%29%26%23178%3B-6%E7%94%B1%E4%BA%8E%282x-1%29%26%23178%3B%E3%80%81%283y%2B2%29%26%23178%3B%E2%89%A50%2C%E6%89%80%E4%BB%A5%E5%8E%9F%E5%A4%9A%E9%A1%B9%E5%BC%8F%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E5%BD%93%282x-1%29%26)
x,y为何值时,多项式4x²+9y²-4x+12y-1有最小值,并求出最小值?4x²+9y²-4x+12y-1=(4x²-4x+1)+(9y²+12y+4)-6=(2x-1)²+(3y+2)²-6由于(2x-1)²、(3y+2)²≥0,所以原多项式的最小值当(2x-1)&
x,y为何值时,多项式4x²+9y²-4x+12y-1有最小值,并求出最小值?
4x²+9y²-4x+12y-1
=(4x²-4x+1)+(9y²+12y+4)-6
=(2x-1)²+(3y+2)²-6
由于(2x-1)²、(3y+2)²≥0,所以原多项式的最小值当(2x-1)²=0且(3y+2)²=0时取得,为-6,
解得此时的x=1/2,y=-2/3,
因此,当x=1/2,y=-2/3时,多项式4x²+9y²-4x+12y-1有最小值为-6.
这答案为什么解得x=1/2,y=2/3
x,y为何值时,多项式4x²+9y²-4x+12y-1有最小值,并求出最小值?4x²+9y²-4x+12y-1=(4x²-4x+1)+(9y²+12y+4)-6=(2x-1)²+(3y+2)²-6由于(2x-1)²、(3y+2)²≥0,所以原多项式的最小值当(2x-1)&
答:
4x²+9y²-4x+12y-1
=(4x²-4x+1)+(9y²+12y+4)-6
=(2x-1)²+(3y+2)²-6
因为:(2x-1)²>=0,(3y+2)²>=0
所以:
4x²+9y²-4x+12y-1=(2x-1)²+(3y+2)²-6>=0+0-6=-6
所以:原多项式的最小值在(2x-1)²=0并且(3y+2)²=0时取得,为-6
所以:
(2x-1)²=0
(3y+2)²=0
所以:
2x-1=0
3y+2=0
解得:x=1/2,y=-2/3