# Simplification - 02

## 01. On simplification the value of 1−11+2–√ + 11−2–√is = ?{\text{1}} - \frac{1}{{1 + \sqrt 2 }}{\text{ + }}\frac{1}{{1 - \sqrt 2 }}{\text{is = ?}}

• 1
$2\sqrt{2}-1$
• 2
$1-2\sqrt{2}$
• 3
$1-\sqrt{2}$
• 4
$-2\sqrt{2}$

## 06.(x+1x)(x−1x)(x2+1x2−1)(x2+1x2+1)$\left(x+\frac{1}{x}\right)\left(x-\frac{1}{x}\right)\left({x}^{2}+\frac{1}{{x}^{2}}-1\right)\left({x}^{2}+\frac{1}{{x}^{2}}+1\right)$\left( {x + \frac{1}{x}} \right)\left( {x - \frac{1}{x}} \right)\left( {{x^2} + \frac{1}{{{x^2}}} - 1} \right)\left( {{x^2} + \frac{1}{{{x^2}}} + 1} \right)         is equal to ?

• 1
${x}^{6}-\frac{1}{{x}^{6}}$
• 2
${x}^{8}-\frac{1}{{x}^{8}}$
• 3
${x}^{6}+\frac{1}{{x}^{6}}$
• 4
${x}^{8}+\frac{1}{{x}^{8}}$

## 07. The expression 1x−1−1x+1−2x2+1−4x4+1$\frac{1}{x-1}-\frac{1}{x+1}-\frac{2}{{x}^{2}+1}-\frac{4}{{x}^{4}+1}$\frac{1}{{x - 1}} - \frac{1}{{x + 1}} - \frac{2}{{{x^2} + 1}} - \frac{4}{{{x^4} + 1}}       is equal to = ?

• 1
$\frac{8}{{x}^{8}+1}$
• 2
$\frac{8}{{x}^{8}-1}$
• 3
$\frac{8}{{x}^{7}-1}$
• 4
$\frac{8}{{x}^{7}+1}$

## 09. If x=3–√ + 2–√,x = \sqrt 3 {\text{ + }}\sqrt 2 {\text{,}}   then the value of x3−1x3${x}^{3}-\frac{1}{{x}^{3}}${x^3} - \frac{1}{{{x^3}}}   is?

• 1
$10\sqrt{2}$
• 2
$14\sqrt{2}$
• 3
$22\sqrt{2}$
• 4
$8\sqrt{2}$
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