2. (a) Given that \(3 ^ { - 1.5 } = a \sqrt { 3 }\) find the exact value of \(a\)
(b) Simplify fully \(\frac { \left( 2 x ^ { \frac { 1 } { 2 } } \right) ^ { 3 } } { 4 x ^ { 2 } }\)
a) \(a = \frac { 3 ^ { - 1.5 } } { \sqrt { 3 } } = \frac { 1 } { 9 }\)
b) \(\frac { \left( 2 x ^ { 1 / 2 } \right) ^ { 3 } } { 4 x ^ { 2 } } = \frac { 2 ^ { 3 } x ^ { 1 / 2 \times 3 } } { 4 x ^ { 2 } } = 2 x ^ { - 1 / 2 }\) Solve the simultaneous equations $$\begin{aligned} & y + 4 x + 1 = 0
& y ^ { 2 } + 5 x ^ { 2 } + 2 x = 0 \end{aligned}$$ $$\begin{aligned} & \text { (1) } y = - 4 x - 1
& \therefore ( - 4 x - 1 ) ^ { 2 } + 5 x ^ { 2 } + 2 x = 0
& \therefore 16 x ^ { 2 } + 8 x + 1 + 5 x ^ { 2 } + 2 x = 0
& \therefore 21 x ^ { 2 } + 10 x + 1 = 0
& x = \frac { - 10 \pm \sqrt { ( - 10 ) ^ { 2 } - 4 ( 21 ) ( 1 ) } } { 2 \times 21 }
&
& x = - 1 / 7 \quad x = - 1 / 3
& \begin{array} { r l } y = - 4 ( - 1 / 7 ) - 1 & y = - 4 ( - 1 / 3 ) - 1
= & - 1 / 7
( - 1 / 7 , - 3 / 7 ) & = 1 / 3 \end{array}
& ( - 1 / 3,1 / 3 ) \end{aligned}$$