If x = 7 - , then is equal to: 1. 14 2. 7 3. 4.

Given, x = 7 - Now, Hence, option 4 is correct option.

Mathematics

If x = 7 - $\sqrt{5}$ , then $x - \dfrac{1}{x}$ is equal to:
14
7
$2\sqrt{5}$
$\dfrac{301 - 45\sqrt{5}}{44}$

Rational Irrational Nos

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Answer

Given, x = 7 - $\sqrt{5}$

$\Rightarrow \dfrac{1}{x} = \dfrac{1}{7 - \sqrt{5}}\\[1em] = \dfrac{1}{7 - \sqrt{5}} \times \dfrac{(7 + \sqrt{5})}{(7 + \sqrt{5})}\\[1em] = \dfrac{7 + \sqrt{5}}{(7)^2 - (\sqrt{5})^2}\\[1em] = \dfrac{7 + \sqrt{5}}{49 - 5}\\[1em] = \dfrac{7 + \sqrt{5}}{44}$

Now,

$\Rightarrow x - \dfrac{1}{x} = 7 - \sqrt{5} - \dfrac{7 + \sqrt{5}}{44}\\[1em] = \dfrac{44(7 - \sqrt{5})}{44} - \dfrac{7 + \sqrt{5}}{44}\\[1em] = \dfrac{308 - 44\sqrt{5} - (7 + \sqrt{5})}{44} \\[1em] = \dfrac{308 - 44\sqrt{5} - 7 - \sqrt{5}}{44} \\[1em] = \dfrac{301 - 45\sqrt{5}}{44} \\[1em]$

Hence, option 4 is correct option.

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Mathematics

If x = 7 - $\sqrt{5}$ , then $x - \dfrac{1}{x}$ is equal to:
14
7
$2\sqrt{5}$
$\dfrac{301 - 45\sqrt{5}}{44}$

Rational Irrational Nos

Answer

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