If a + 1/(a + 2) = 4 Then find , (a + 2)2 + 1/((a + 2)^2)

Given = a + \(\frac{1}{a + 2}\) = 4

By adding 2 on both sides we get,

(a + 2) + \(\frac{1}{a + 2}\) = 4 + 2 = 6

(a + 2)² + \(\frac{1}{(a + 2)^2}\) = 6² - 2 = 34

 

If x + \(\frac{1}{x}\) = a

then, x² + \(\frac{1}{x^2}\) = a² - 2