Question

solve it....
step bystep explanation​

Answer 1

$\large\underline{ \underline{ \sf{ \red{given:} }}}$

$\sf{ {x}^{2} + \frac{1}{ {x}^{2} } = 6 }$

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}} \\ \\ \sf \: {x}^{4} + \frac{1}{ {x}^{4} }$

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

$\sf \: {x}^{2} + \frac{1}{ {x}^{2}} = 6 \\ \\ \\ \rm \: squaring \: both \: sides..... \\ \\ \\ \sf \: ({x}^{2} + { \frac{1}{ {x}^{2} } )}^{2} = {6}^{2} \\ \\ \\ \boxed{ \bf \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}$

Here ,

• a = x²

• b = 1/x²

Putting values ,

$\\ \sf{( {x}^{2}) }^{2} + {( \frac{1}{ {x}^{2} } )}^{2} + 2( \cancel{ {x}^{2}} )( \frac{1}{ \cancel{{x}^{2} }} ) = 36 \\ \\ \\ \sf \: {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 36 \\ \\ \\ \underline{ \boxed{ \sf \: \green{{x}^{4} + \frac{1}{ {x}^{4} } = 34}}}$

More identities :-

• ( a - b )² = a² + b² + 2ab

• ( a - b )( a + b ) = a² - b²

• ( a + x )( a + y ) = a² + ( x + y ) + xy