Question

x +1/x = 4 , find the values of the following [ i ] x - 1 /x​

Answer 1

The Value of x = ⅓

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Answer 2

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{x + \dfrac{1}{x} = 4} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{x - \dfrac{1}{x} }  \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

$\tt \:  ⟼ {(x + y)}^{2} - {(x - y)}^{2} = 4xy$

$\large\underline\purple{\bold{Solution :- }}$

❖ We know that

$\tt \:  {(x + y)}^{2} - {(x - y)}^{2} = 4xy$

$\bf \:  Replace \: y \: by \: \frac{1}{x} \: we \: get$

$\tt \: :   ⟼ {(x + \dfrac{1}{x} )}^{2} - {(x - \dfrac{1}{x}) }^{2} = 4 \times x \times \dfrac{1}{x}$

$\tt \ \: :  ⟼ {4}^{2} - {(x - \dfrac{1}{x} )}^{2} = 4 \: \: \: [ \because \: x \: + \dfrac{1}{x} = 4]$

$\tt \ \: :  ⟼ 16 - {(x - \dfrac{1}{x}) }^{2} = 4$

$\tt \ \: :  ⟼ {(x - \dfrac{1}{x}) }^{2} = 16 - 4$

$\tt \ \: :  ⟼ {(x - \dfrac{1}{x} )}^{2} = 12$

$\tt \ \: :  ⟼ x - \dfrac{1}{x} = \sqrt{12}$

$\tt \ \: :  ⟼ x - \dfrac{1}{x} = 2 \sqrt{3}$