(a) Given the simultaneous equations

\(\lg x+2\lg y=1,\)

\(x-3y^2=13,\)

(i) show that \(x^2-13x-30=0\).

(ii) Solve these simultaneous equations, giving your answers in exact form.

(b) Solve the equation

\(\log_a x+3\log_x a=4,\)

where \(a\) is a positive constant, giving \(x\) in terms of \(a\).