Inequality with two variables For x, y \in \mathbb{R}, find the

Kailey Perez

Kailey Perez

Answered question

2022-04-23

Inequality with two variables
For x, yR, find the maximum of
P=2xy(xy+1)+(x+y)(xy1)(1+x2)(1+y2)

Answer & Explanation

Genevieve James

Genevieve James

Beginner2022-04-24Added 12 answers

If x=y we obtain a value 4+334, where the equality occurs for x=2+3.
Thus, it's enough to prove that
2xy(xy+1)+(x+y)(xy1)(1+x2)(1+y2)4+334,
which is a quadratic inequality of y

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