Question

please anyone answer this question ..... x+1/x =5 then find x-1/x​

Answer 1

Answer:

Required numeric value of x - 1 / x is ±√21.

Step-by-step explanation:

Two methods are given to solve this.

Method 1

= > ( x + 1 / x ) = 5

Square on both sides :

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

= > x^2 + ( 1 / x )^2 + 2( x × 1 / x ) = 25 { ( a + b )^2 = a^2 + b^2 + 2ab }

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

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

= > x^2 + 1 / x^2 = 23

Adding - 2 to both sides :

= > x^2 + 1 / x^2 - 2 = 23 - 2

= > x^2 + 1 / x^2 - 2( 1 ) = 23 - 2

= > x^2 + 1 / x^2 - 2 ( x × 1 / x ) = 21

= > ( x - 1 / x )^2 = 21 { using a^2 + b^2 - 2ab = ( a - b )^2 }

= > x - 1 / x = ±√21

Hence the required numeric value of x - 1 / x is ±√21

Method 2

From the properties of expansion :

• ( a + b )^2 - ( a - b )^2 = 4ab

Thus,

= > ( x + 1 / x )^2 - ( x - 1 / x )^2 = 4( x × 1 / x )

= > ( 5 )^2 - ( x - 1 / x )^2 = 4

= > 25 - ( x - 1 / x )^2 = 4

= > 25 - 4 = ( x - 1 / x )^2

= > 21 = ( x - 1 / x )^2

= > ±√21 = x - 1 / x

Hence the required numeric value of x - 1 / x is ±√21.