Question

If a = root8 + root7, then find the value of a^2 - 2+ 1/a^2

Answer 1

Answer:

a = 8+3√7   b = 1/a  ⇒ 1/8+3√7

                                ⇒ 8-3√7/1  (on rationalizing)

now,    a = 8+3√7    b = 8-3√7

 ∴  a²+b² = (8+3√7)² + (8-3√7)²

              =  (64 + 63+48√7) + (64 + 63 - 48√7)

      a²+b² =   254