1.
If $$\frac{a}{b} = \frac{{25}}{6}{\text{,}}$$   then the value of $$\frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}}$$   is?

2.
If $$a = \frac{{\sqrt 3 - \sqrt 2 }}{{\sqrt 3 + \sqrt 2 }}$$    and $$b = \frac{{\sqrt 3 + \sqrt 2 }}{{\sqrt 3 - \sqrt 2 }}{\text{,}}$$    then the value of $$\frac{{{a^2}}}{b}$$  + $$\frac{{{b^2}}}{a}$$  = ?

3.
The simplified value of following is: $$\left( {\frac{3}{{15}}{a^5}{b^6}{c^3} \times \frac{5}{9}a{b^5}{c^4}} \right)$$     $$ ÷ $$ $$\frac{{10}}{{17}}{a^2}b{c^3}$$

4.
If p(x + y)2 = 5 and q(x - y)2 = 3, then the simplified value of p2(x + y)2 + 4pqxy - q2(x - y)2 is?

5.
If $$x + \frac{1}{x} = 3{\text{,}}$$   where $$x \ne 0{\text{,}}$$  then the value of $$\frac{{{x^4} + 3{x^3} + 5{x^2} + 3x + 1}}{{{x^4} + 1}}$$     = ?

6.
If x = 1 + $$\sqrt 2 $$  + $$\sqrt 3 $$  and y = 1 + $$\sqrt 2 $$  - $$\sqrt 3 {\text{,}}$$  then the value of $$\frac{{{x^2} + 4xy + {y^2}}}{{x + y}}$$   is?

7.
If x : y = 3 : 5 and x - y = -2, then the value of x + y is?

8.
If $${\left( {a + \frac{1}{a}} \right)^2} = 3{\text{,}}$$    then find the value of $${a^{30}}$$ + $${a^{24}}$$ + $${a^{18}}$$ + $${a^{12}}$$ + $${a^6}$$ + $$1$$ = ?

9.
If a + b + c = 26 and ab + bc + ca = 109, find the value of a2 + b2 + c2 = ?

10.
Find the minimum value of x which the expression x3 - 7x2 + 11x - 5 ≥ 0.

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