(a)[3]
Complete the table entries.
(b)[5]
On the grid, sketch the graph of $y = \frac{x^2}{2} + \frac{1}{x^2} - \frac{2}{x}$ for $-3 \le x \le -0.3$ and $0.2 \le x \le 3$.
(c)[2]
Use your graph to solve $\frac{x^2}{2} + \frac{1}{x^2} - \frac{2}{x} \le 0$.
(d)[1]
Determine the smallest positive integer value of $k$ for which $\frac{x^2}{2} + \frac{1}{x^2} - \frac{2}{x} = k$ has two solutions for $-3 \le x \le -0.3$ and $0.2 \le x \le 3$.
(e(i))[3]
By drawing an appropriate straight line, solve $\frac{x^2}{2} + \frac{1}{x^2} - \frac{2}{x} = 3x + 1$ for $-3 \le x \le -0.3$ and $0.2 \le x \le 3$.
(e(ii))[3]
The equation $\frac{x^2}{2} + \frac{1}{x^2} - \frac{2}{x} = 3x + 1$ may be rewritten as $x^4 + ax^3 + bx^2 + cx + 2 = 0$. Find the values of $a$, $b$ and $c$.