If a + 1/(a + 7) = 3 Then find , (a + 7)3 + 1/((a + 7)^3)

Given = a + \(\frac{1}{a + 7}\) = 3

By adding 7 on both sides we get,

(a + 7) + \(\frac{1}{a + 7}\) = 3 + 7 = 10

(a + 7)³ + \(\frac{1}{(a + 7)^3}\) = 10³ - 3 × 10 = 970

 

Note - if x +  \(\frac{1}{x}\) = a

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