Question

a^3 + 2ab^2/2a^2b + b^3=123/136

Answer 1

(a³ + 2ab² )/(2a²b + b³) = 123/136

or, 136(a³ + 2ab²) = 123(2a²b + b³)

or, 136a³ + 272ab² = 246a²b + 123b³

or, 136a³/b³ + 272ab²/b³ = 246a²b/b³ + 123b³/b³

or, 136(a/b)³ + 272(a/b) = 246(a/b)² + 123

Let us consider (a/b) = x

then, 136x³ + 272x = 246x² + 123

or, 136x³ + 272x - 246x² - 123 = 0

or, 136x(x² + 2) - 123(x² + 2) = 0

or, (136x - 123)(x² + 2) = 0

x² + 2 ≠ 0 so, 136x - 123 = 0

hence, x = 123/136

therefore, a/b = 123/136