x^2+y^2=2(x+y) 则x+y的最大值是

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x^2+y^2=2(x+y) 则x+y的最大值是
x^2+y^2=2(x+y) 则x+y的最大值是

x^2+y^2=2(x+y) 则x+y的最大值是
令x+y=a
y=a-x
代入
x²+a²-2ax+x²=2a
2x²-2ax+(a²-2a)=0
x是实数则方程有实数解
△>=0
4a²-8a²+16a>=0
4a(a-4)≤0
0≤a≤4
所以最大值是4

x+y的最大值为4

用线性规划。原式化为x^2-2x+y^2-2y=0
(x-1)^2+(y-1)^2=2，即为圆心（1,1），半径为根号二的圆
然后设z=x+y，线性规划啊
楼主高中了应该知道

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