Question

If 2x+3y=12 and xy=6 then find 8x^3 + 27y^3

Answer 1

8x³ + 27y³ = (2x)³ + (3y)³.

Now a³ + b³ = (a + b)(a² + b² - ab)

(2x + 3y)² = 4x² + 9y² + 12ab.

Or 4x² + 9y² = 144 - 72 = 72

Now substitute the values. You will get 12 x 66 = 792