Given m² + m = \(\dfrac{1}{4}\), find the value of 8m⁴ + 20m³ + 13m².

Suppose a + b = 5 and a³ + b³ = 35, find the value of a² + b².

If 3x + 5y + 3 = 0 find the value of 8^3x+2 . 32^y

If a^x + a^-x = 3, find the value of a^2x + a^-2x.