Question

X4+1/x4=119 then find x+1/x=(?)

Answer 1

Answer:

Required value of x + 1 / x is √13.

Step-by-step explanation:

Given,

x^4 + 1 / x^4 = 119

Adding 2 to both sides :

= > x^4 + 1 / x^4 + 2 = 119 + 2

= > ( x^2 )^2 + ( 1 / x^2 )^2 + 2 = 121

= > ( x^2 )^2 + ( 1 / x^2 )^2 + 2( x^2 × 1 / x^2 ) = 121

= > ( x^2 + 1 / x^2 )^2 = 121 { a^2 + b^2 + 2ab = ( a + b )^2 }

= > x^2 + 1 / x^2 = 11

Again adding 2 to both sides :

= > x^2 + 1 / x^2 + 2 = 11 + 2

= > x^2 + 1 / x^2 + 2( x × 1 / x ) = 13

= > ( x + 1 / x )^2 = 13

= > x + 1 / x = √13

Hence the required value of x + 1 / x is √13.