If $\dfrac{x}{a} = \dfrac{y}{b} = \dfrac{z}{c}$, show that :

$\dfrac{x^3}{a^3} + \dfrac{y^3}{b^3} + \dfrac{z^3}{c^3} = \dfrac{3xyz}{abc}$.

If b is the mean proportion between a and c, show that :

$\dfrac{a^4 + a^2b^2 + b^4}{b^4 + b^2c^2 + c^4} = \dfrac{a^2}{c^2}$

If x and y both are positive and (2x² - 5y²) : xy = 1 : 3, find x : y.

Find x, if $16\Big(\dfrac{a - x}{a + x}\Big)^3 = \dfrac{a + x}{a - x}$