设实数x.y满足3x^2+2y^2

题目

设实数x.y满足3x^2+2y^2

答案

令2x+y=p
y=p-2x
3x^2+2y^2-6
=3x^2+2(p-2x)^2-6
=11x^2-8px+2p^2-6
≤0
△=64p^2-4*11(2p^2-6)
=-24p^2+24*11
≥0
p^2≤11
-√11≤p≤√11
p=2x+y的最大值：√11