51. The factors of x4 + x2 + 25 are:
52. The value of [(a2 - b2)3 + (b2 - c2)3 + (c2 - a2)3] ÷ [(a - b)3 + (b - c)3 + (c - a)3] is equal to: (Given a ≠ b ≠ c).
53. What is the value of $$\frac{{\left( {{a^2} + {b^2}} \right)\left( {a - b} \right) - \left( {{a^3} - {b^3}} \right)}}{{{a^2}b - a{b^2}}}?$$
54. If $${x^4} + \frac{1}{{{x^4}}} = 14159,$$ then the value of $$x + \frac{1}{x}$$ is:
55. If $$2x + \frac{1}{{2x}} = 2,$$ then what is the value of $$\sqrt {2{{\left( {\frac{1}{x}} \right)}^4} + {{\left( {\frac{1}{x}} \right)}^5}} ?$$
56. If x = 32.5, y = 34.6 and z = 30.9, then the value x3 + y3 + z3 - 3xyz of is 0.98k, where k is equal to:
57. If $$\frac{{{a^2} + {b^2} + {c^2} - 1024}}{{ab - bc - ca}} = - 2$$ and a + b = 5c, where c > 0, then the value of c is . . . . . . . .
58. If x = 2 + √3, y = 2 - √3, z = 1 then what is the value of $$\frac{x}{{yz}} + \frac{y}{{xz}} + \frac{z}{{xy}} + 2\left[ {\frac{1}{x} + \frac{1}{y} + \frac{1}{z}} \right]?$$
59. If $$\frac{1}{{{x^2} + {a^2}}} = {x^2} - {a^2},$$ then the value of x is:
60. If 9x2 + y2 = 37 and xy = 2, x, y > 0, then the value of (27x3 + y3) is:
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