因式分解x²+x-72 -x²-6x+10 若x、y满足2x+y-4=0求xy的最大值
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因式分解x²+x-72 -x²-6x+10 若x、y满足2x+y-4=0求xy的最大值
![因式分解x²+x-72 -x²-6x+10 若x、y满足2x+y-4=0求xy的最大值](/uploads/image/z/12554224-16-4.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3x%26%23178%3B%2Bx-72+-x%26%23178%3B-6x%2B10+%E8%8B%A5x%E3%80%81y%E6%BB%A1%E8%B6%B32x%2By-4%3D0%E6%B1%82xy%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC)
x²+x-72
=(x+9)(x-8)
-x²-6x+10
=-(x²+6x-10)
=-(x²+6x+9-19)
=-[(x+3)²-19]
=-(x+3+√19)(x+3-√19)
2x+y-4=0
∴y=4-2x
xy=x(4-2x)
=-2x²+4x
=-2(x²-2x+1)+2
=-2(x-1)²+2
∴x=1,y=2时有最大值2
=(x+9)(x-8)
-x²-6x+10
=-(x²+6x-10)
=-(x²+6x+9-19)
=-[(x+3)²-19]
=-(x+3+√19)(x+3-√19)
2x+y-4=0
∴y=4-2x
xy=x(4-2x)
=-2x²+4x
=-2(x²-2x+1)+2
=-2(x-1)²+2
∴x=1,y=2时有最大值2
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