x²+xy+y²=1由均值不等式得x²+y²≥2xy2xy+xy≤1xy≤1/3(x+y)²-xy=1(x+y)²=1+xy≤1+1/3=4/3-2√3/3≤x+y≤2√3/3x+y的最大值为2√3/3
1/3开方
2/3
