Question

If $\: \: \: \: \: \: \: \: \: \: \: \: {x}^{2} + \frac{1}{ {x}^{2} } = 3$ then find the value of x-1/x ​

Answer 1

$\: \: \: \: \:{\large{\pmb{\sf{\underline{ Here's \: your \: required \: solution!! }}}}}$

Here, we are given that :-

$\: \: \: \: \: \: \: \: \: \sf \purple{:\implies {\: \: \: {x}^{2} + \dfrac{1}{ {x}^{2} } = 3}}$

According to the question, we are asked to find out the value of :-

$\: \: \: \: \: \: \: \: \: \sf \purple {:\implies \: \: \: x - \dfrac{1}{x}}$

⠀⠀⠀ ______________________

We know that :-

$\sf:\implies\green {\: {(a + b)}^{2} - {(a - b)}^{2} = 4ab}$

$\sf :\implies\:{\bigg(x + \dfrac{1}{x} \bigg) }^{2} - {\bigg(x - \dfrac{1}{x} \bigg) }^{2} = 4 \times x \times \dfrac{1}{x}$

$\sf :\implies\: {(3)}^{2} - {\bigg(x - \dfrac{1}{x} \bigg) }^{2} = 4$

$\sf :\implies\:9 - {\bigg(x - \dfrac{1}{x} \bigg) }^{2} = 4$

$\sf :\implies\:9 - 4 = {\bigg(x - \dfrac{1}{x} \bigg) }^{2}$

$\sf :\implies\:5 = {\bigg(x - \dfrac{1}{x} \bigg) }^{2}$

$\sf:\implies \underline\green {{ \:x - \dfrac{1}{x} = \pm \: \sqrt{5}}}$

Answer 2

Answer:

The above answer is correct