- (a) Use binomial expansions to show that \(\sqrt { \frac { 1 + 4 x } { 1 - x } } \approx 1 + \frac { 5 } { 2 } x - \frac { 5 } { 8 } x ^ { 2 }\)
A student substitutes \(x = \frac { 1 } { 2 }\) into both sides of the approximation shown in part (a) in an attempt to find an approximation to \(\sqrt { 6 }\)
(b) Give a reason why the student should not use \(x = \frac { 1 } { 2 }\)
(c) Substitute \(x = \frac { 1 } { 11 }\) into
$$\sqrt { \frac { 1 + 4 x } { 1 - x } } = 1 + \frac { 5 } { 2 } x - \frac { 5 } { 8 } x ^ { 2 }$$
to obtain an approximation to \(\sqrt { 6 }\). Give your answer as a fraction in its simplest form.