If a + 1/(a + 4) = 5 Then find , (a + 4)3 + 1/((a + 4)^3)

Given = a + \(\frac{1}{a + 4}\) = 5

By adding 4 on both sides we get,

(a + 4) + \(\frac{1}{a + 4}\) = 5 + 4 = 9

(a + 4)³ + \(\frac{1}{(a + 4)^3}\) = 9³ - 3 × 9 = 702

 

Note - if x +  \(\frac{1}{x}\) = a

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