If a + 1/(a + 3) = 12 Then find , (a + 3)2 + 1/((a + 3)^2)

Given = a + \(\frac{1}{a + 3}\) = 12

By adding 3 on both sides we get,

(a + 3) + \(\frac{1}{a + 3}\) = 12 + 3 = 15

(a + 3)² + \(\frac{1}{(a + 3)^2}\) = 15² - 2 = 223

 

Note - if x +  \(\frac{1}{x}\) = a

then x² + \(\frac{1}{x^2}\) =  a² - 2