21. If a = 1 + √3, b = 1 - √3, then what is the value of a2 + b2?
22. If $$A = \frac{{0.216 + 0.008}}{{0.36 + 0.04 - 0.12}}$$ and $$B = \frac{{0.729 - 0.027}}{{0.81 + 0.09 + 0.27}},$$ then what is the value of (A2 + B2)2?
23. If 2x2 - 7x + 5 = 0, then what is the value of $${x^2} + \frac{{25}}{{4{x^2}}}?$$
24. If 4pxy = (x + 2y)2 - (x - 2y)2, then what will be the value of p?
25. If 3x2 - 9x + 3 = 0, then what is the value of $${\left( {x + \frac{1}{x}} \right)^3}?$$
26. If $$x - \frac{1}{x} = 1,$$ then what is the value of $$\frac{1}{x}\left( {\frac{1}{{x - 1}} - \frac{1}{{x + 1}} + \frac{1}{{{x^2} + 1}} - \frac{1}{{{x^2} - 1}}} \right)?$$
27. If 2x2 + 5x + 1 = 0, then one of the value of $$x - \frac{1}{{2x}}$$ is:
28. If x4 - 6x2 - 1 = 0, then the value of $${x^6} - 5{x^2} + \frac{5}{{{x^2}}} - \frac{1}{{{x^6}}} + 5$$ is:
29. If a + b + c = -11, then what is the value of (a + 4)3 + (b + 5)3 + (c + 2)3 - 3(a + 4)(b + 5)(c + 2)?
30. If $$x - \frac{1}{x} = 5,$$ x ≠ 0, then what is the value of $$\frac{{{x^6} + 3{x^3} - 1}}{{{x^6} - 8{x^3} - 1}}?$$
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