1. If $$x + \frac{1}{x} = 1,$$ then the value of x12 + x9 + x6 + x3 + 1 is:
2. If (3 + 2√5)2 = 29 + K√5, then what is the value of K?
3. What is the simplified value of $$\frac{{\left( {x + y + z} \right)\left( {xy + yz + zx} \right) - xyz}}{{\left( {x + y} \right)\left( {y + z} \right)\left( {z + x} \right)}}?$$
4. If 3x2 - 5x + 1 = 0, then the value of $$\left( {{x^2} + \frac{1}{{9{x^2}}}} \right)$$ is:
5. If $${x^2} + \frac{1}{{{x^2}}} = \frac{7}{4}$$ for x > 0 then what is the value of $${x^4} + \frac{1}{{{x^4}}}.$$
6. If a4 + 1 = $$\left[ {\frac{{{{\text{a}}^2}}}{{{{\text{b}}^2}}}} \right]$$ (4b2 - b4 - 1), then what is the value of a4 + b4?
7. If x1x2x3 = 4(4 + x1 + x2 + x3), then what is the value of $$\left[ {\frac{1}{{2 + {x_1}}}} \right] + \left[ {\frac{1}{{2 + {x_2}}}} \right] + \left[ {\frac{1}{{2 + {x_3}}}} \right]?$$
8. The value of $$\frac{{\left( {0.545} \right)\left( {0.081} \right)\left( {0.51} \right)\left( {5.2} \right)}}{{{{\left( {0.324} \right)}^3} + {{\left( {0.221} \right)}^3} - {{\left( {0.545} \right)}^3}}}{\text{is:}}$$
9. If x + y + z = 19, xy + yz + zx = 144, then the value of $$\sqrt {{x^3} + {y^3} + {z^3} - 3xyz} $$ is:
10. If $$\sqrt {\left( {{a^2} + {b^2} + ab} \right)} + \sqrt {\left( {{a^2} + {b^2} - ab} \right)} = 1,$$ then what is the value of (1 - a2) (1 - b2) ?
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