find the value of x
Answers
Answer:
Required values of x are : ±1 , 2 - 1 / 2.
Step-by-step explanation:
Here,
= > 2( x^2 + 1 / x^2 ) - 3( x - 1 / x ) - 4 = 0
= > 2( x^2 + 1 / x^2 ) - 4 - 3( x - 1 / x ) = 0
= > 2( x^2 + 1 / x^2 - 2 ) - 3( x - 1 / x ) = 0
= > 2{ x^2 + 1 / x^2 - 2( 1 ) } - 3( x - 1 / x ) = 0
= > 2{ x^2 + 1 / x^2 - 2( x × 1 / x ) } - 3( x - 1 / x ) = 0 { x × 1 / x = 1 }
From factorisation :
- a^2 + b^2 - 2ab = ( a - b )^2
Thus, here,
- x^2 + 1 / x^2 - 2( x × 1 / x ) = ( x - 1 / x )^2
= > 2( x - 1 / x )^2 - 3( x - 1 / x ) = 0
= > ( x - 1 / x ) [ 2( x - 1 / x ) - 3( 1 ) ] = 0
= > ( x - 1 / x ) [ 2( x - 1 / x ) - 3 ] = 0
Since their product is 0, one of them must be 0.
Case 1 : If x - 1 / x is 0 :-
= > x - 1 / x = 0
= > x = 1 / x
= > x^2 = 1
= > x = ±√1
= > x = ±1 ( or + 1 & - 1 )
Case 2 : If 2( x - 1 / x ) - 3 is 0 :-
= > 2( x - 1 / x ) - 3 = 0
= > 2( x - 1 / x ) = 3
= > 2( x^2 - 1 ) / x = 3
= > 2x^2 - 2 = 3x
= > 2x^2 - 3x - 2 = 0
= > 2x^2 - ( 4 - 1 )x - 2 = 0
= > 2x^2 - 4x + x - 2 = 0
= > 2x( x - 2 ) + ( x - 2 ) = 0
= > ( x - 2 )( 2x + 1 ) = 0
Since their product is 0, one of them must be 0.
If x - 2 is 0 = > x - 2 = 0 = > x = 2
If 2x + 1 is 0 = > 2x + 1 = 0 = > 2x = - 1 = > x = - 1 / 2.
Required values of x are : ±1 , 2 - 1 / 2.