Question

已知实数x,y满足x的平方+3x+y=3,求x+y的最大值 要详细过程

Answer 1

x²+3x+y=3.===>(x²+2x+1)+(x+y)=4.===>x+y=4-(x+1)²≤4.等号仅当x=-1,y=5时取得，∴(x+y)max=4.

Answer 2

X^2+3X+y=3
y=-X^2-3X+3
X+y=X-X^2-3X+3
=-X^2-2X+3
当X=-1时
〈X十y）max=-1+2+3=4