Question

x+1/x=2 then x4+1/x4=?

Answer 1

Ans

Given
x+1/x=2
x^2+1=2x
x^2-2x-1=0

»x=1,-1

»x^4+1/x^4
»1^4+1/1^4
»1+1=2

Answer 2

Given,

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

Therefore,

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

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

or,$(x^{2} +\frac{1}{x^{2} }) -2.x^{2}.\frac{1}{x^{2} }$

or, $(x+\frac{1}{x} )^{2} -2.x.\frac{1}{x}.-2$

or, $2^{2}-2-2$

or, $4-4$

or, $0$

The required answer is $0$