Question

if x=5-2√6, 5hen find the value ofx^2+1/x^2​

Answer 1

${ \tt{ \huge \underline{ question \colon}}}$

${ \rm{ \large{if \: x = 5 - 2 \sqrt{6} }}}$

${ \rm{ \large{then \: find \: the \: value \: of \: {x}^{2} + \dfrac{1}{ {x}^{2} } }}}$

${ \tt{ \huge \underline{ solution \colon}}}$

${ \rm{ {\: x = 5 - 2 \sqrt{6} }}}$

${ \rm{ \therefore {x}^{2} + \dfrac{1}{ { {x}^{2} } } }}$

${ \rm{ = {(5 - 2 \sqrt{6}) }^{2} + \dfrac{1}{ { {(5 - 2 \sqrt{6}) }^{2} } } }}$

${ \rm{ = {25 - 4 \times 6 } + \dfrac{1}{ { {25 - 4 \times 6 } } } }}$

${ \rm{ = {126 } + \dfrac{1}{ { {126 } } } }}$

${ \rm{ = \dfrac{15877}{ { {126 } } } }}$

${ \rm{ = 126.00}}$

${ \tt{the \: value \: of \: {x}^{2} + \dfrac{1}{ {x}^{2} } \: is = 126.00}}$

Answer 2

$\huge\underline\bold\red{Answer}$

$\: x \: = \: 5 \: - \: 2 \sqrt{6} \\ {x}^{2} + \frac{1}{ {x}^{2} } \\ =5 \: - 2 \sqrt{ {6}^{2} } \: + \frac{1}{5 - 2 \ \sqrt{ {6}^{2} } } \\ 25 \: - 4 \: \times \: 6 \: + \frac{1}{25 - 4 \times 6} \\ = 126 \: + \frac{1}{126} \\ \frac{15877}{126} \\ = 126.0 \\ the \: value \: of \: {x}^{2} + \: \frac{1}{ {x \: }^{2} } \: is \: 126.0$

Hope it helps uhh