3[a - \({1{} \over a}\)] + [a - \({{1} \over a}\)]³ = ?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 2)

Answer 1

Formula used:

a³ - \({{1} \over a}\)³ = (a - b)[ a² + \({{1} \over a^2}\) + 1]

Calculations:

⇒ 3[a - \({1{} \over a}\)] + [a - \({{1} \over a}\)]³

⇒ (a - \({1{} \over a}\)) [ 3 + (a - \({{1} \over a}\))2 ]

⇒ (a - \({1{} \over a}\)) [ 3 + a2 + \({{1} \over a^2}\) - 2 ]

⇒ (a - \({1{} \over a}\)) [ a2 + \({{1} \over a^2}\) + 1]

⇒ a3 - \({{1} \over a^{3}}\)

⇒ Hence, The value of the above equation is a3 - \({{1} \over a^3}\)