If a + 1/(a + 7) = 5 Then find , (a + 7)2 + 1/((a + 7)^2)

Given = a + \(\frac{1}{a + 7}\) = 5

By adding 7 on both sides we get,

(a + 7) + \(\frac{1}{a + 7}\) = 5 + 7 = 12

(a + 7)² + \(\frac{1}{(a + 7)^2}\) = 12² - 2 = 142

 

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

then, x² + \(\frac{1}{x^2}\) = a² - 2