Algebra MCQs

If $$x + \left( {\frac{1}{x}} \right) = 2{\text{,}}$$   then the value of $${x^7}{\text{ + }}\left( {\frac{1}{{{x^5}}}} \right)$$   is?

If a² + a + 1 = 0, then the value of a⁹ is?

If $$c + \frac{1}{c} = \sqrt 3 {\text{,}}$$   then the value of $${c^3} + \frac{1}{{{c^3}}}$$   is equal to?

If $$\sqrt {\left( {1 - {p^2}} \right)\left( {1 - {q^2}} \right)} = \frac{{\sqrt 3 }}{2},$$     then what is the value of $$\sqrt {2{p^2} + 2{q^2} + 2pq} + \sqrt {2{p^2} + 2{q^2} - 2pq} \,?$$

The value of $$\frac{1}{{{a^2} + ax + {x^2}}}$$   $$ - $$ $$\frac{1}{{{a^2} - ax + {x^2}}}$$   $$ + $$ $$\frac{2ax}{{{a^4} + {a^2}{x^2} + {x^4}}}$$    is?

If P = 7 + 4√3 and PQ = 1, then what is the value of $$\frac{1}{{{P^2}}} + \frac{1}{{{Q^2}}}?$$

If x⁴ + x^-4 = 194, x > 0, then what is the value of $$x + \frac{1}{x} + 2?$$

If $${\text{A}} = \frac{{{{\left( {0.1} \right)}^3} + {{\left( {0.2} \right)}^3} + {{\left( {0.3} \right)}^3} + 3\left( {0.005 + 0.016 + 0.027} \right) + 0.036}}{{{{\left( {0.1} \right)}^2} + {{\left( {0.2} \right)}^2} + {{\left( {0.3} \right)}^2} + 0.04 + 0.06 + 0.12}}$$            then the value of 60A is:

If x = y = z, then $$\frac{{{{\left( {x + y + z} \right)}^2}}}{{{x^2} + {y^2} + {z^2}}}$$   is?