Question

if x-1/x=3 then find x^2+1/x^2 please show it along with process

Answer 1

Hey there!

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Given :

$x - \frac{1}{x} = 3$

To find :

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

So,

$x - \frac{1}{x} = 3 \\ \\ \bold{on \: squaring \: both \: sides - } \\ \\ (x - \frac{1}{x} ) {}^{2} = (3) {}^{2} \\ \\ \bold{using \: identity...} \\ \\ \bold{(a - b) {}^{2} = a {}^{2} + b {}^{2} - 2ab } \\ \\ x {}^{2} + \frac{1}{x {}^{2} } - 2 \times \cancel x \times \frac{1}{ \cancel x} = 9 \\ \\ x {}^{2} + \frac{1}{x {}^{2}} - 2 = 9 \\ \\ x {}^{2} + \frac{1}{x {}^{2}} = 9 + 2 \\ \\ \boxed{ \bold{x {}^{2} + \frac{1}{x {}^{2}} = 11}}$

Hence, the value found.
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Thanks for the question!

Answer 2

Hey there !

Given : x - 1/x = 3

To find : x² + 1 / x²

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

$x - \frac{1}{x} = 3 \\ \\ \bold{on \: squaring \: both \: sides \: - } \\ \\ (x - \frac{1}{x} ) {}^{2} = (3) {}^{2} \\ \\ \boxed{ \bold{using \: identity \: - }} \\ \boxed{ \bold{(a - b) {}^{2} = a {}^{2} + b {}^{2} - 2ab }}$

Now, we have ;

$x {}^{2} + \frac{1}{x {}^{2} } - 2 \times \cancel x \times \frac{1}{ \cancel x} = 9 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } - 2 = 9 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 9 + 2 \\ \\ \boxed {\boxed{ \bold{x {}^{2} + \frac{1}{x {}^{2} } = 11}}}$
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Thanks for the question !