Solve $x^x = 2^{3x+192}$

Let $a, b, c \in\mathbf{R}^+$ and $\frac{a^2}{1+a^2}+\frac{b^2}{1+b^2}+\frac{c^2}{1+c^2}=1$, show that $$abc\le\frac{\sqrt{2}}{4}$$

Solve $\sqrt{x+5}=x^2-5$.

Solve $x^2 + x - 2= x\sqrt{2x^2-3}$.

Find all $a$ such the the equation $\frac{ax-2}{x-2}=3$ has no solution.