51. If a3 = 117 + b3 and a = 3 + b, then the value of a + b is?
52. If $${x^2} + \frac{1}{{{x^2}}} = 98{\text{,}}$$ $$\left( {x > 0} \right){\text{,}}$$ then the value of $$x^3 + \frac{1}{{{x^3}}}$$ is?
53. If x = y + z then x3 - y3 - z3 is?
54. If a + b + c + d = 4, then the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$ + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$ + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$ + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$ is?
55. If x - 11, then the value of x5 - 12x4 + 12x3 - 12x2 + 12x - 1 is?
56. If $$a + \frac{1}{b}$$ = $$b + \frac{1}{c}$$ = $$c + \frac{1}{a}$$ (where a ≠ b ≠ c), then abc is equal to?
57. If x, y, z are the three factors of a3 - 7a - 6, then value of x + y + z will be?
58. If p3 + q3 + r3 - 3pqr = 4, and a = q + r, b = r + p and c = p + q, then what is the value of a3 + b3 + c3 - 3abc?
59. If x = $$a + \frac{1}{a}$$ and y = $$a - \frac{1}{a}$$ then $$\sqrt {{x^4} + {y^4} - 2{x^2}{y^2}} $$ is equal to:
60. If x4 + y4 + x2 + y2 = $$17\frac{1}{{16}}$$ and x2 - xy + y2 = $$5\frac{1}{4},$$ then one of the values of (x - y) is:
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