Question

if x+1/x=2then find x4 +1x4.
mind power Question❓​

Answer 1

$\large\star\boxed{\bf{\green{\underline{\underline{GIVEN:-}}}}}$

$x + \frac{1}{x} = 2$

$\large\star\boxed{\sf{\green{To \:Find:-}}}$

${x}^{4} + \frac{1}{ {x}^{4} }$

$\large\star\boxed{\bf{\green{SOLUTION:-}}}$

FIRST WE HAVE TO FIND

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

BECAUSE IT IS GIVEN THAT

$x + \frac{1}{x} = 2$

SO,

$= > ( {x + \frac{1}{x} })^{2} = {x}^{2} + \frac{1}{{x}^{2} } + 2.x. \frac{1}{x}$

$as \: x \: and \: \frac{1}{x} \: gets \: cancelled \: we \: get$

$= > {2 }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2$

$= > 4 - 2 = {x}^{2} + \frac{1}{ {x}^{2} }$

$so \: {x}^{2} + \frac{1}{ {x}^{2} } = 2$

$now \: as \: we \: have \: got \: {x}^{2} + \frac{1}{ {x}^{2} } = 2 \: we \: have \: to \: find \: {x}^{4} + \frac{1}{ {x}^{4} }$

$( {x}^{2} + \frac{1}{ {x}^{2} } )^{2} = 2$

$= > ( {x}^{2} + \frac{1}{ {x}^{2} } ) ^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2. {x}^{2}. \frac{1}{ {x}^{2} }$

$as \: {x}^{2} \: and \: \frac{1}{ {x}^{2} } \: gets \: cancelled \: we \: get \:$

$= > ( {x}^{2} + \frac{1}{ {x}^{2} } ) ^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2$

$= > {2}^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2$

$= > 4 - 2= {x}^{4} + \frac{1}{ {x}^{4} }$

$so \: {x}^{4} + \frac{1}{ {x }^{4} } = 2$

THEREFORE THE RIGHT ANS IS 2.

$actual \: answer \: of \: {x}^{4} + \frac{1}{ {x}^{4} } \: is \: 2$