Question

ifa = √2 + 1 / √2 - 1 and b = √2 - 1 / √2 + 1 then find the value of a^2 + b^2 -4ab

Answer 1

a = r2 + 1 / r2 - 1

b = r2 - 1 / r2 + 1

Solve: a^2 + b^2 - 4ab

If we write that out completely...

((sqrt 2 + 1) / (sqrt 2 - 1))^2 + ((sqrt 2 - 1) / (sqrt 2 + 1))^2 - 4 * ((sqrt 2 + 1) / (sqrt 2 - 1)) * ((sqrt 2 - 1) / (sqrt 2 + 1))

If we solve that using regular calculation rules and, where applicable, a calculator. The result is 30.

Check with answer sheet / calculator.