If x ≠ 0 and $x + \dfrac{1}{x} = 2$; then show that :

$x^2 + \dfrac{1}{x^2} = x^3 + \dfrac{1}{x^3} = x^4 + \dfrac{1}{x^4}$.

If 2x - 3y = 10 and xy = 16, find the value of 8x³ - 27y³.

Expand (3x - 5y - 2z)(3x - 5y + 2z)

The sum of two numbers is 9 and their product is 20. Find the sum of their :

(i) squares

(ii) cubes.