Question

Give step by step explanation.. ​

Answer 1

( a³ + 2ab² ) / ( 2a²b + b³ ) = 123 / 136

136 ( a³ + 2ab² ) = 123 ( 2a²b + b³ )

136a³ + 272ab² = 246a²b + 123b³

Divide LHS and RHS by b³.

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

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

Let, a/b = x, so in above equation,

136x³ + 272x = 246x² + 123

136x³ + 272x - 246x² - 123 = 0

Take, 136 and 123 common out as shown,

136x(x² + 2) - 123(x² + 2) = 0

Separating the commons,

(136x - 123)(x² + 2) = 0

x² + 2 cant be equal to 0 so,

136x - 123 = 0

x = 123/136

Since, x = a/b = 123/136

From proportionality law, a = 123 , b = 136.