# Solving an exponential inequality problem

How do I prove the following inequality :

$$\Bigg(\frac{2}{\alpha^2} \, \big( e^{\alpha x} - e^{\alpha y} \big) \, + \, e^{\alpha y} (y^2 - x^2) \; \Bigg) > 0$$

given, $x, y > 0$ ?

Here, $\alpha$ is a positive constant.
• This is obviously false, try $x=y+1$ when $y\to\infty$. – Did Jun 16 '16 at 5:22