51. If a + b = 1, c + d = 1 and a - b = $$\frac{d}{c}{\text{,}}$$ then the value of c2 - d2 = ?
52. If x = 3t, y = $$\frac{1}{2}$$(t + 1), then the value of t for which x = 2y is?
53. If $${x^2} + \frac{1}{5}x + {a^2}$$ is a perfect square, then a is?
54. If (x - 1) and (x + 3) are the factors of x2 + k1x + k2 then-
55. If $$\frac{{5x}}{{2{x^2} + 5x + 1}} = \frac{1}{3},$$ then the value of $$\left( {x + \frac{1}{{2x}}} \right) = \,?$$
56. If $$x > 1$$ and $${x^2} + \frac{1}{{{x^2}}} = 83,$$ then the $${x^3} - \frac{1}{{{x^3}}}\,{\text{is?}}$$
57. If $${\left( {a + \frac{1}{a}} \right)^2}\, = 3$$ then $${a^3} + \frac{1}{{{a^3}}} = ?$$
58. If x + y + z = 6 and x2 + y2 + z2 = 20, then the value of x3 + y3 + z3 - 3xyz is?
59. If x = a - b, y = b - c, z = c - a, then the numerical value of the algebraic expression x3 + y3 + z3 - 3xyz will be?
60. If (x - a)(x - b) = 1 and a - b + 5 = 0, then the value of $${\left( {x - a} \right)^3}$$ - $$\frac{1}{{{{\left( {x - a} \right)}^3}}}\,{\text{}}$$ is?
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