Question

if (x-1/4)=5,find the values of (1) (x2+1/x2) and (2) (x4+1/x4).​

Answer 1

Your question needs a correction.

Correct Question : x - 1 / x = 5

Answer:

x^2 + 1 / x^2 = 27 and x^4 + 1 / x^4 is 727.

Step-by-step explanation:

Given,

x - 1 / x = 5

Square on both sides :

= > ( x - 1 / x )^2 = 5^2

From the properties of expansion :

• ( a - b )^2 = a^2 + b^2 - 2ab

= > ( x )^2 + ( 1 / x )^2 - 2( x × 1 / x ) = 25

= > x^2 + 1 / x^2 - 2( 1 ) = 25

= > x^2 + 1 / x^2 - 2 = 25

= > x^2 + 1 / x^2 = 25 + 2

= > x^2 + 1 / x^2 = 27

Again square on both sides :

= > ( x^2 + 1 / x^2 )^2 = 27^2

= > ( x^2 )^2 + ( 1 / x^2 )^2 + 2( x^2 × 1 / x^2 ) = 729

= > x^4 + 1 / x^4 + 2( 1 ) = 729

= > x^4 + 1 / x^4 + 2 = 729

= > x^4 + 1 / x^4 = 729 - 2

= > x^4 + 1 / x^4 = 727

Hence,

x^2 + 1 / x^2 = 27 and x^4 + 1 / x^4 is 727.