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
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
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