若x,y是正数,则(x+1/2y)^2+(y+1/2x)^2的最小值是?

Answer 1

此题可用不等式来解
(X+1/2Y)^2+(Y+1/2X)^2>=2(X＋1/2Y)(Y+1/2X)=2*(XY+1+1/4XY)
而XY+1/4XY>=1,所以最小值是4