Solving $\sqrt\frac{x^2+2x-2}{x^2+3x+2} + \sqrt\frac{x^2+3x+2}{x^2+2x-2}=\frac52 $ Got these two problems on an exam recently and was unsure if I managed to answer them correctly:
$$\sin^4x + \cos^4x \ge \frac58, \ x \in \left\{-\frac\pi4,\frac\pi4\right\}$$
Second:
$$\sqrt\frac{x^2+2x-2}{x^2+3x+2} + \sqrt\frac{x^2+3x+2}{x^2+2x-2}=\frac52 $$
Anyone able to provide the correct answer or method of solving these?

For the first, start from $\sin^2x+\cos^2x=1$ and square both sides.
For the second, note that the second part is the reciprocal of the first. So you need to solve $p+\frac 1p=\frac 52$ first.
But what have you tried?
