If the fourth proportional to $a^2-ab+b^2, a^3+b^3$ and $a-b$ is $a^k-b^k$, then $k=$_____.

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

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