(a) If \(\frac{\sqrt{5} + 4}{3 - 2\sqrt{5}} - \frac{2 + \sqrt{5}}{4 - 2\sqrt{5}} = a + b\sqrt{5}\), find the values of a and b. (b)(i) Evaluate : \(\begin{v...

(a) If \(\frac{\sqrt{5} + 4}{3 - 2\sqrt{5}} - \frac{2 + \sqrt{5}}{4 - 2\sqrt{5}} = a + b\sqrt{5}\), find the values of a and b.

(b)(i) Evaluate : \(\begin{vmatrix} 2 & -1 & 2 \\ 1 & 3 & 4 \\ 1 & 2 & 1 \end{vmatrix}\)

(ii) Using the result in b(i), find, correct to two decimal places, the value of x in the system of equations.

\(2x - y + 2z + 5 = 0\)

\(x + 3y + 4z - 1 = 0\)

\(x + 2y + z + 2 = 0\)