1. If $${64^{x + 1}} = \frac{{64}}{{{4^x}}}{\text{,}}$$ then the value of x is?
2. If ax2 + bx + c = a(x - p)2, then the relation among a, b, c would be?
3. If a2 + b2 + c2 + 3 = 2(a + b + c) then the value of (a + b + c) is?
4. If $$x - \frac{1}{x} = 5{\text{,}}$$ then $${x^2}{\text{ + }}\frac{1}{{{x^2}}}$$ is?
5. If $$n = 7 + 4\sqrt 3 {\text{,}}$$ then the value of $$\left( {\sqrt n + \frac{1}{{\sqrt n }}} \right)$$ is:
6. If $$x = \sqrt 3 + \sqrt 2 {\text{,}}$$ then the value of $$\left( {x + \frac{1}{x}} \right)\,{\text{is?}}$$
7. If p + q = 10 and pq = 5, then the numerical value of $$\frac{p}{q}{\text{ + }}\frac{q}{p}$$ will be?
8. If x = 3 + 2$$\sqrt 2 $$ and xy = 1, then the value of $$\frac{{{x^2} + 3xy + {y^2}}}{{{x^2} - 3xy + {y^2}}}$$ is?
9. If x - y = 2, xy = 24, then the value of (x2 + y2) is?
10. If the expression $$\frac{{{x^2}}}{{{y^2}}} + tx + \frac{{{y^2}}}{4}$$ is a perfect square, then the value of t is?
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