Question

Find x
$x = \frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } + \frac{ \sqrt{3 } - 1}{ \sqrt{3} + 1} find \: value \: of \: {x}^{2} + { \frac{253}{x} }^{2}$

Answer 1

$<b >Hey here is your answer$

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$x = \frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } + \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } \\ \\ now \: \\ \\ = \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \\ \\ = \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ = \frac{(2 + \sqrt{3} {)}^{2} }{( {2)}^{2}- { \sqrt{(3)} }^{2} } \\ \\ = \frac{ {(2)}^{2} + {( \sqrt{3} )}^{2} + 2 \times 2 \times \sqrt{3} }{4 - 3} \\ \\ = \frac{4 + 3 + 4 \sqrt{3} }{1} \\ \\ = 4 + 3 + 4 \sqrt{3} \\ \\ = 7 + 4 \sqrt{3} \\ \\ now \: \\ \\ = \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \\ \\ = \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ = \frac{ {(2 - \sqrt{3} )}^{2} }{ {(2)}^{2} - { (\sqrt{3} )}^{2} } \\ \\ = \frac{ {(2)}^{2} + {( \sqrt{3} )}^{2} -2 \times 2 \times \sqrt{3} }{4 - 3} \\ \\ = \frac{4 + 3 - 4 \sqrt{3} }{1} \\ \\ = 7 - 4 \sqrt{3} \\ \\ now \: \\ \\ = \frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1} \\ \\ = \frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1 }{ \sqrt{3} - 1} \\ \\ = \frac{ {( \sqrt{3} - 1) }^{2} }{ {( \sqrt{3}) }^{2} - {(1)}^{2} } \\ \\ = \frac{ {( \sqrt{3}) }^{2} + {(1)}^{2} - 2 \times \sqrt{3} \times 1}{3 - 1} \\ \\ = \frac{3 + 1 - 2 \sqrt{3} }{2} \\ \\ = \frac{4 -2 \sqrt{3} }{2} \\ \\ = 2 - \sqrt{3} \\ \\ now \: x \: = \: \\ \\ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } + \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } \: \\ \\ = 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} + 2 - \sqrt{3} \\ \\ = 16 - \sqrt{3} \\ \\ \\ now \: \\ \\ put \: this \: value \: of \: x \: in \: the \: equation \: \\ \\ {x}^{2} + (\frac{253}{x} {)}^{2} \\ \\ {(16 - \sqrt{3} )}^{2} + \frac{253}{{(16-\sqrt3)}^{2}} \\ \\ (16)^2 + (\sqrt3)^2 - 2× 16 × \sqrt3 + \frac{253}{{(16^2 + {\sqrt3}^2) - 2 × 16 × \sqrt3}} \\ \\ 256 + 3 - 32\sqrt3 + \frac{253}{{(256 + 3 - 32\sqrt3)}} \\ \\ 259 - 32\sqrt3 + \frac{253}{(259 - 32\sqrt3)}$

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hope this helps you

### BE BRAINLY ###

Answer 2

Answer:

i think that above user's has give verified answer so.....I think that if answer then it is also of no use