6. In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
- Given that
$$2 x y - 3 x ^ { 2 } = 50$$
and
$$y - x ^ { 3 } + 6 x = 0$$
show that
$$2 x ^ { 4 } - 15 x ^ { 2 } - 50 = 0$$
- Hence solve the simultaneous equations
$$\begin{aligned}
2 x y - 3 x ^ { 2 } & = 50
y - x ^ { 3 } + 6 x & = 0
\end{aligned}$$
Give your answers in fully simplified surd form.
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