Question

x+1/x =4 find the value of x-1/x​

Answer 1

$Given \: x + \frac{1}{x} = 4 \: --(1)$

$\boxed { \pink { (a-b)^{2} = (a+b)^{2} - 4ab }}$

$\Big( x - \frac{1}{x}\Big)^{2} \\= \Big( x +\frac{1}{x}\Big)^{2} - 4 \times x \times \frac{1}{x} \\= 4^{2} - 4 \\= 16 - 4 \\= 12$

$Now ,\red { Value \:of \: x - \frac{1}{x}} = \pm \sqrt{12} \\= \pm 2\sqrt{3}$

Therefore.,

$\red { Value \:of \: x - \frac{1}{x}}\green {= \pm 2\sqrt{3}}$

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