Pinko wrote:
If x and y are real numbers, determine the greatest possible value of the expression
(x+1)(y+1)(xy+1)(x2+1)(y2+1).
We have:
(x2+1)2(y2+1)2=(x2+1)(y2+1)(x2+1)(y2+1)≥(x+1)2(y+1)2(xy+1)24Therefore:
(x+1)(y+1)(xy+1)(x2+1)(y2+1)≤2Equality at x=y=1