Math, asked by khushuragni, 7 months ago

If ^4 + 1 ^4 = 142, find the value of 2 + 1/ 2

Answers

Answered by Mihir1001

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$\Large{ {x}^{4} + \frac{1}{ {x}^{4} } = 142}$

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

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

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QUADRATIC equations

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

We have,

$\Large{ \longmapsto {x}^{4} + \frac{1}{ {x}^{4} } = 142}$

$\Large{ \Rightarrow {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 142 + 2}$ ————[ adding 2 to both the sides ]

$\Large{ \Rightarrow {( {x}^{2} )}^{2} + { \left( \frac{1}{ {x}^{2} } \right) }^{2} + 2( {x}^{4} ) \left( \frac{1}{ {x}^{4} } \right) = 144}$

$\Large{ \Rightarrow { \left( {x}^{2} + \frac{1}{ {x}^{2} } \right) }^{2} = 144}$ ———— $\left[ \because {a}^{2} + {b}^{2} + 2(a)(b) = {(a + b)}^{2} \right]$

$\Large{ \Rightarrow { \left( {x}^{2} + \frac{1}{ {x}^{2} } \right) }^{2} = {(12)}^{2} }$

$\Large{ \Rightarrow {x}^{2} + \frac{1}{ {x}^{2} } = 12 }$ ————[ on square-rooting both the sides ]

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

$\Large{ \Rightarrow {x}^{2} + \frac{1}{ {x}^{2} } = 12 }$

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