Question

(x + 1/x) = 6, find the values of (x-1/x)
find the values of )​

Answer 1

hope this answer helps you!!

Answer 2

Given :

• x + 1/x = 6

To Find :

• Value of x - 1/x

Solution :

$\tt x + \frac{1}{x} = 6 \\ \\ \tt By \: squaring \: both \: side \\ \\ \tt \implies \bigg( {x + \frac{1}{x} \bigg) }^{2} = {6}^{2} \\ \\ \tt \implies {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 36 \\ \\ \tt \implies {x}^{2} + \frac{1}{ {x}^{2} } = 34 \\ \\ \tt Subtract \: 2 \: from \: both \: side \\ \\ \tt \implies {x}^{2} + \frac{1}{ {x}^{2}} - 2 = 34 - 2 \\ \\ \tt \implies { \bigg(x - \frac{1}{x} \bigg) }^{2} = 32 \\ \\ \tt \implies x - \frac{1}{x} = \sqrt{32} \\ \\ \tt \implies x - \frac{1}{x} = 4\sqrt{2}$

$\large\underline{ \tt \green{Value \: of \: x - \frac{1}{x} \: is \: 4\sqrt{2} }}$