Question

if x - 1/ x = 2 ,then find the value of x^4 +1/x^4. please answer me it is urgent​

Answer 1

GIVEN :-

$\implies \rm{ \dfrac{x - 1}{x} = 2}$

TO FIND :-

VALUE OF

$\implies \rm{ \dfrac{ {x}^{4} + 1}{ {x}^{4} } }$

SOLUTION :-

$\implies \rm{ \dfrac{x - 1}{x} = 2}$

$\implies \rm{ x - 1 = 2x}$

$\implies \rm{ - 1 = 2x - x}$

$\implies \boxed{\rm{ x = - 1}}$

now we know the value of X

now we are putting the value of X

$\implies \rm{ \dfrac{ {( - 1)}^{4} + 1}{ {( - 1)}^{4} } }$

$\implies \rm{ \dfrac{ 1 + 1}{ 1 } }$

$\implies \rm{ \dfrac{2}{ 1 } }$

$\implies \boxed{ \boxed{\rm{ \dfrac{ {x}^{4} + 1}{ {x}^{4} } = 2}}}$

ALTERNATIVE METHOD :-

FOR ,

$\implies \boxed{ \rm{ \bf{\dfrac{x + 1}{x} = 2}}}$

$\implies \rm{ \dfrac{x + 1}{x} = 2}$

now breaking terms

$\implies \rm{ \dfrac{x }{x} + \dfrac{1}{x} = 2}$

$\implies \rm{ x + \dfrac{1}{x} = 2}$

now multiplying the eq by X both side

$\implies \rm{ x {}^{2} + \dfrac{x}{x} = 2x}$

$\implies \rm{ x {}^{2} + 1 = 2x}$

$\implies \rm{ x {}^{2} - 2x + 1 = 0}$

now by using quadratic formula

$\implies \boxed{ \rm{x = \dfrac{ - b  ±\sqrt{ {b}^{2} - 4ac }}{2a} }}$

where ,

b = -2

a = 1

c = 1

$\implies \rm{x = \dfrac{ - b  ±\sqrt{ {b}^{2} - 4ac }}{2a} }$

$\implies \rm{x = \dfrac{ - ( - 2)  ±\sqrt{ {( -2)}^{2} - 4( 1)( 1) }}{2(1)} }$

$\implies \rm{x = \dfrac{ 2  ±\sqrt{ 4 - 4( 1)( 1) }}{2(1)} }$

$\implies \rm{x = \dfrac{ 2  ±\sqrt{ 4 - 4 }}{2(1)} }$

$\implies \rm{x = \dfrac{ 2  ±0}{2} }$

$\implies \rm{x = \dfrac{ 2 }{2} }$

$\implies \boxed{\rm{x = 1 }}$

now put the value of X

$\implies \rm{ \dfrac{ {( 1)}^{4} + 1}{ {( 1)}^{4} } }$

$\implies \rm{ \dfrac{ ( 1)+ 1}{ ( 1) }}$

$\implies \rm{ \dfrac{ 2}{ 1 } }$

$\implies \boxed{ \boxed{\rm{ \dfrac{ {x}^{4} + 1}{ {x}^{4} } = 2}}}$