Question

若实数x，y满足x2＋y2＋xy＝1，则x＋y的最大值是

Answer 1

令x+y=a
y=a-x
代入
x²+a²-2ax+x²+ax-x²=1
x²-ax+(a²-1)=0
x是实数则△>=0
a²-4a²+4>=0
a²<=4/3
-2√3/3<=a<=2√3/3
所以最大值是2√3/3

Answer 2

1）x2＋y2＋xy＝1，x2＋y2>=2xy 得1>=3xy, xy<=(1/3)
2) x2＋y2＋xy＝1 可得x2＋y2＋2xy＝1+xy
(x+y)2<=(4/3) ......