41. If (8x3 - 27y3) ÷ (2x - 3y) = (Ax2 + Bxy + Cy2), then the value of (2A + B - C) is:
42. If the equation k(21x2 + 24) + rx + (14x2 - 9) = 0
k(7x2 + 8) + px + (2x2 - 3) = 0 have both roots common, then the value of $$\frac{p}{r}$$ is:
k(7x2 + 8) + px + (2x2 - 3) = 0 have both roots common, then the value of $$\frac{p}{r}$$ is:
43. If xy = -6 and x3 + y3 = 19 (x and y are integers), then what is the value of $$\frac{1}{{{x^{ - 1}}}} + \frac{1}{{{y^{ - 1}}}}?$$
44. If a2 + b2 + c2 + 84 = 4(a - 2b + 4c), then $$\sqrt {ab - bc + ca} $$ is equal to:
45. The value of $$\frac{{{{\left( {4.6} \right)}^4} + {{\left( {5.4} \right)}^4} + {{\left( {24.84} \right)}^2}}}{{{{\left( {4.6} \right)}^2} + {{\left( {5.4} \right)}^2} + 24.84}}$$ is:
46. If ab + bc + ca = 8 and a2 + b2 + c2 = 20, then a possible value of $$\frac{1}{2}$$(a + b + c)[(a - b)2 + (b - c)2 + (c - a)2] is:
47. If a2 + b2 + c2 + 27 = 6(a + b + c), then what is the value of $$\root 3 \of {{a^3} + {b^3} - {c^3}} ?$$
48. If x2 - √7x + 1 = 0, then what is the value of $${x^5} + \frac{1}{{{x^5}}}?$$
49. If $$x + \frac{1}{{16x}} = 3,$$ then the value of $$16{x^3} + \frac{1}{{256{x^3}}}$$ is:
50. If $$x + \frac{1}{x} = 5,$$ then what is the value of $${x^6} + \frac{1}{{{x^6}}}?$$
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