# University Maths Solution

Maths Question
Question 1

$\text{Solve 4}\sqrt{x+2}-\sqrt{x+7}-5\sqrt{x-1}=0$

Question 2

\begin{align} & \text{Solve }x\sqrt{2+x}+2\sqrt{2-x}=\sqrt{8+{{x}^{3}}} \\ & \\\end{align}

Question 3

$\text{Simplify }\frac{1}{\sqrt{3}+\sqrt{2}}$

Question 4

$\text{Simplify}\frac{2-2\sqrt{2}+\sqrt{5}}{2-2\sqrt{2}-\sqrt{5}}$

Question 5

$\text{Find the square root of }17+12\sqrt{2}$

Question 6

$\text{Find the positive square root of }19-4\sqrt{21}$

Question 7

Given that $a=\frac{1}{2-\sqrt{3}}$ , $b=\frac{1}{2+\sqrt{3}}$ , find the value of ${{a}^{2}}+{{b}^{2}}$

Question 8

Simplify as much as possible $\frac{1}{\sqrt{x+1}-\sqrt{x-1}}$

Question 9

Simplify as much as possible ${{\left( \sqrt{x}+\frac{1}{\sqrt{x}} \right)}^{2}}-{{\left( \,\sqrt{x}-\frac{1}{\sqrt{x}} \right)}^{2}}$

Question 10

Simplify as much as possible $\frac{1}{x-\sqrt{{{x}^{2}}-1}}$

Question 11

Simplify without table, find the value of $\frac{1}{{{(1-\sqrt{3})}^{2}}}-\frac{1}{{{(1+\sqrt{3})}^{2}}}$