31. If a + a2 + a3 - 1 = 0, then what is the value of $${a^3} + \frac{1}{a}?$$
32. If $$x\left( {3 - \frac{2}{x}} \right) = \frac{3}{x},$$ then the value of $${x^3} - \frac{1}{{{x^3}}}$$ is equal to:
33. If $$\frac{{{x^8} + 1}}{{{x^4}}} = 14,$$ then the value of $$\frac{{{x^{12}} + 1}}{{{x^6}}}$$ is:
34. If $$\frac{{x + y}}{z} = 2,$$ then what is the value of $$\left[ {\frac{y}{{y - z}}} \right] + \left[ {\frac{x}{{x - z}}} \right]?$$
35. If $$x + \frac{{16}}{x} = 8,$$ then the value of $${x^2} + \frac{{32}}{{{x^2}}}$$ is:
36. If $$x + 3y - \frac{{2z}}{4} = 6,\,x + \frac{2}{3}\left( {2y + 3z} \right) = 33$$ and $$\frac{1}{7}$$(x + y + z) + 2z = 9 then what is the value of 46x + 131y?
37. If $$\sqrt x + \frac{1}{{\sqrt x }} = 3,$$ then the value of $${x^3} + \frac{1}{{{x^3}}}$$ is:
38. If a + b = 5 and ab = 3, then (a3 + b3) is equal to:
39. If (4a - 3b) = 1, ab = $$\frac{1}{2}$$ where a > 0 and b > 0, what is the value of (64a3 + 27b3)?
40. If (5√5x3 - 81√3y3) ÷ (√5x - 3√3y) = (Ax2 + By2 + Cxy), then the value of (6A + B - $$\sqrt {15} $$ C) is:
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