31. If $$a = \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}}$$ & $$b = \frac{{\sqrt 5 - 1}}{{\sqrt 5 + 1}}{\text{,}}$$ then the value of $$\frac{{{a^2} + ab + {b^2}}}{{{a^2} - ab + {b^2}}}{\text{ is?}}$$
32. If a = 4.36, b = 2.39 and c = 1.97, then the value of a3 - b3 - c3 - 3abc is?
33. If $$\frac{{3a + 5b}}{{3a - 5b}} = 5,$$ then a : b is equal to?
34. If x : y = 3 : 4, then (7x + 3y) : (7x - 3y) is equal to?
35. For what value (s) of a is $$x + \frac{1}{4}\sqrt x + {a^2}$$ a perfect square?
36. If x, y are two positive real number and $${x^{\frac{1}{3}}} = {y^{\frac{1}{4}}},$$ then which of the following relations is true?
37. If $$x = \frac{{\sqrt 3 }}{2}{\text{,}}$$ then $$\frac{{\sqrt {1 + x} }}{{1 + \sqrt {1 + x} }}{\text{ + }}$$ $$\frac{{\sqrt {1 - x} }}{{1 - \sqrt {1 - x} }}$$ is equal to?
38. If for non-zero, x, x2 - 4x - 1 = 0, the value of $${x^2} + \frac{1}{{{x^2}}}$$ is?
39. $$\left( {x + \frac{1}{x}} \right)$$ $$\left( {x - \frac{1}{x}} \right)$$ $$\left( {{x^2} + \frac{1}{{{x^2}}} - 1} \right)$$ $$\left( {{x^2} + \frac{1}{{{x^2}}} + 1} \right)$$ is equal to?
40. If a2x+2 = 1, where is a positive real number other than 1, then x is equal to?
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