31. If $${x^2} + {y^2} = 29$$ and xy = 10 where x > 0, y > 0, x > y, then the value of $$\frac{{x + y}}{{x - y}}$$ is?
32. If $${p^2} + {q^2} = 7pq{\text{,}}$$ then the value of $$\frac{p}{q}{\text{ + }}\frac{q}{p}$$ is equal to?
33. If $$x = {3^{\frac{1}{3}}} - {3^{ - \frac{1}{3}}}$$ value of $$3{x^3} + 9x$$ is?
34. If xy(x + y) = m, then the value of x3 + y3 + 3m is?
35. $$p + \frac{1}{{p + 2}} = 1{\text{,}}$$ Find the value of $${\left( {p + 2} \right)^3}$$ $$+$$ $$\frac{1}{{{{\left( {p + 2} \right)}^3}}}$$ $$-$$ 3 = ?
36. If $$x + \frac{1}{x} \ne 0$$ and $${x^3} + \frac{1}{{{x^3}}} = 0{\text{,}}$$ then the value $${\left( {x + \frac{1}{x}} \right)^4}$$ is?
37. If $$x + \frac{1}{x} = 2$$ then $${x^2} + \frac{1}{{{x^2}}}$$ is equal to?
38. If x + y = √3 and x - y = √2, then the value of 8xy(x2 + y2) is?
39. If $$\left( {x + \frac{1}{x}} \right)$$ : $$\left( {x - \frac{1}{x}} \right)$$ = 5 : 3 the value of x is/are ?
40. If p3 - q3 = (p - q){(p -q)2 + xpq}, then the value of x is?
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