Question

if x+1/x=16 find the value of x^2+1/x^2

Answer 1

$\huge{ \underline{ \bold{ \orange{ \mathfrak{question}}:}}}$

if x+1/x=16 find the value of x^2+1/x^2

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$\bold{ \overline{ \underline{ \underline{ \red{final \: answer}}}}:} </p><p>$

${ \green{ \bold{ \mathbb{ {x}^{2} + \frac{1}{ {x}^{2} } = \frac{50626}{225} }}}}$

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$\huge \underline \bold \red{SOLUTION}:$

${\huge {⇝}} \frac{x + 1}{x} = 16 \\ {\huge {⇝}} 1 + \frac{1}{x} = 16 \\ {\huge {⇝}} \frac{1}{x} = 15 \\{\huge {⇝} }x = \frac{1}{15} \\ lets \: find \: the \: value \: of \: {x }^{2} + \frac{1}{ {x}^{2} } \\ by \: substituting \: the \: value \: of \: x \\ {\huge {⇝}} {x}^{2} + \frac{1}{ {x}^{2} } \\ {\huge {⇝}} \frac{1}{ {15}^{2} } + \frac{1}{ ( { \frac{1}{15} )}^{2} } \\ {\huge {⇝}} \frac{1}{225} + 225 \\ \: \: \: \: \: \: \: \: { \green{\bold {⇝\frac{50626}{225} }}}$

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