Using componendo and dividendo, find the value of $x$ in the equation 

$\frac{\sqrt{3x+4}+\sqrt{3x-5}}{\sqrt{3x+4}-\sqrt{3x-5}}=9$.

If $a, b$ and $c$ are in continued proportion, then prove that

$\frac{a+b+c}{a-b+c}=\frac{{\displaystyle {\left(a+b+c\right)}^2}}{a^2+b^2+c^2}$.

Find the mean proportional of ${\left(a^4-b^4\right)}^2$ and $\left[\right(a^2+b^2\left)\right(a+b){]}^{-2}$.

Find the third proportional to

$16$ and $36$.

The third proportional to ${\left(x^2+y^2+xy\right)}^2$ and $\left(x^3-y^3\right)$ is ${\left(x-y\right)}^k$, find $k$.