Math, asked by praneeldev3, 10 months ago


 x -  \frac{1}{x}  = 5 \\ x {}^{2}  -  \frac{1}{x { }^{2} }  = what

Answers

Answered by Anonymous
1

\huge{\mathfrak{\green{Ans}}} {\mathfrak{wer \: :}}

\Large{\underline{\sf{Given \: }}} \sf{:}

\sf{x - \frac{1}{x} = 5}

\rule{200}{2}

\Large{\underline{\sf{To \: Find }}} \sf{:}

We have to find the value of

\sf{x^2 + \frac{1}{x^2}}

\rule{200}{2}

\Large{\underline{\sf{Solution \: }}} \sf{:}

\sf{x - \frac{1}{x} = 5} ....... ①

(Squaring Both sides) in eq ①

\sf{(x - \frac{1}{x})^2 = (5)^2}

Using Identity :

\Large{\star{\boxed{\sf{(a - b)^2 = a^2 + b^2 - 2ab}}}}

____________[Put Values]

\sf{→x^2 + (\frac{1}{x})^2 - 2(x)(\frac{1}{x}) = 25} \\ \\ \sf{→x^2 + \frac{1}{x^2} - 2(\cancel{x})(\frac{1}{\cancel{x}}) = 25} \\ \\ \sf{→x^2 + \frac{1}{x^2} - 2 = 25} \\ \\ \sf{→x^2 + \frac{1}{x^2} = 25 + 2} \\ \\ \sf{→x^2 + \frac{1}{x^2} = 27}

\Large{\star{\boxed{\sf{x^2 + \frac{1}{x^2} = 27}}}}

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