41. If $$x = 3 + 2\sqrt 2 {\text{,}}$$ then the value of $${x^2}{\text{ + }}\frac{1}{{{x^2}}}{\text{ is?}}$$
42. If $$x\left( {3 - \frac{2}{x}} \right) = \frac{3}{x}{\text{,}}$$ then the value of $${x^2}{\text{ + }}\frac{1}{{{x^2}}}$$ is?
43. If x2 - 3x + 1 = 0, then the value of $${x^2} + x + \frac{1}{x} + \frac{1}{{{x^2}}}$$ is?
44. If a2 + b2 = 5ab, then the value of $$\left( {\frac{{{a^2}}}{{{b^2}}}{\text{ + }}\frac{{{b^2}}}{{{a^2}}}} \right)$$ is?
45. If xy + yz + zx = 0, then $$\left( {\frac{1}{{{x^2} - yz}} + \frac{1}{{{y^2} - zx}} + \frac{1}{{{z^2} - xy}}} \right)$$ $$\left( {x,y,z \ne 0} \right) = ?$$
46. If a + b + c = 9 (where a, b, c are real numbers) then the minimum value of a2 + b2 + c2 is?
47. If a2 + b2 + 4c2 = 2(a + b - 2c) - 3 and a, b, c are real, then the value of (a2 + b2 + c2) is?
48. If $$\frac{{x - {a^2}}}{{b + c}}$$ + $$\frac{{x - {b^2}}}{{c + a}}$$ + $$\frac{{x - {c^2}}}{{a + b}}$$ = 4(a + b + c), then x = ?
49. If $$\frac{a}{b} = \frac{4}{5}$$ and $$\frac{b}{c} = \frac{{15}}{{16}}{\text{,}}$$ then $$\frac{{18{c^2} - 7{a^2}}}{{45{c^2} + 20{a^2}}}$$ is equal to?
50. If $$x \ne 0,$$ $$y \ne 0$$ and $$z \ne 0$$ and $$\frac{1}{{{x^2}}}$$ + $$\frac{1}{{{y^2}}}$$ + $$\frac{1}{{{z^2}}}$$ = $$\frac{1}{{xy}}$$ + $$\frac{1}{{yz}}$$ + $$\frac{1}{{zx}}$$ then the relation among x, y, z is?
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