x+y的最大值是√5,x^2+y^2的最小值2
3x＾2＋2y＾2＝6
y^2=(6-3x^2)/2
t=x^2+y^2
=x^2+(6-3x^2)/2
=x^2+3-3x^2/2
=-x^2/2+3.
容易知道,当x=0,t有最大值为t=3.
当3x^2=6,即x^2=2时候,有最小值,t=-2/2+3=-1+3=2.
令x+y=t
y=t-x
所以 3x^2+2(t-x)^2=6
5x^2-4tx+2t^2-6=0
△=16t^2-20(2t^2-6)≥0
4t^2-5(2t^2-6)≥0
6t^2≤30
t^2≤5
-√5≤t≤√5