Radical Equations

A pendulum's period $T$ (in seconds) is given by $T = \sqrt{L + 5}$, where $L$ is the length in meters. For a certain pendulum, the period equals $(L - 1)$ seconds. Find the length $L$ that satisfies this condition.

Solve the equation: $\sqrt{x+4} + \sqrt{x-3} = 5$.

The concentration $x$ (in mol/L) of a chemical satisfies $\sqrt{x + \sqrt{x}} = 3$. Find $x$.