Do not use a calculator in this question.

(a) Simplify

\(\frac{5+6\sqrt5}{6+\sqrt5}.\)

(b) Show that

\(3^{0.5}\times(\sqrt2)^7\)

can be written in the form \(a\sqrt b\), where \(a\) and \(b\) are integers and \(a\gt b\).

(c) Solve the equation

\(x+\sqrt2=\frac{4}{x},\)

giving your answers in simplest surd form.