Question

已知x，y∈R,x+y=10,求xy的最大值。怎么做急急急

Answer 1

x+y=10，则y=10-x，xy=x*（10-x）=-x^2+10x=-(x^2-10x+25)+25=-(x-5)^2+25,所以xy最大值为25

Answer 2

x+y=10 y=10-x
xy=x(10-x)=-x^2+10x=-(x^2-10x+25)+25=-(x-5)^2+25
因为（x-5）^2>=0 所以-（x-5）^2<=0 -(x-5)^2+25<=25
xy最大值为25

Answer 3

(x+y)²=x²+2xy+y²=10²=100
x²+y² = 100-2xy

x²+y² ≥ 2xy
100-2xy ≥2xy

100 ≥4xy

xy≤25
xy最大值25