Question

if x+1/x=5find x^4 +1/x^4​

Answer 1

Answer:

hey mate here is ur answer hope u find it helpful

Answer 2

Answer:

$\boxed{\bold{\mathsf{{x}^{4} + \frac{1}{ {x}^{4} } =527}}}$

Step-by-step explanation:

Given

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

To find:

$x + \frac{1}{x} = 5$

Apply squaring

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

Now put in the known values

${5}^{2} = {x}^{2} + \frac{1}{{x}^{2} } + 2 \\ \\ 25 - 2 = {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 23$

Now again square both sides

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

Now again put in the known values

${23}^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \\ \\ 529 = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \\ \\ 529 - 2 = {x}^{4} + \frac{1}{ {x}^{4} } \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 527$

$\rule{200}{1}$

⏩$\boxed{\underline{\underline{\bold{\mathsf{Identities\:used}}}}}$:-

❇(a + b)² = a² + b² + 2ab