If a + 1/(a + 1) = 5 Then find , (a + 1)3 + 1/((a + 1)^3)

Given = a + \(\frac{1}{a + 1}\) = 5

By adding 1 on both sides we get,

(a + 1) + \(\frac{1}{a + 1}\) = 5 + 1 = 6

(a + 1)³ + \(\frac{1}{(a + 1)^3}\) = 6³ - 3 × 1 = 213

 

Note - if x +  \(\frac{1}{x}\) = a

then x³ + \(\frac{1}{x^3}\) =  a³ - 3a