Question

If x2 - 5x-1 = 0, find the value of x2 +
1/x2
​

Answer 1

Answer:

Required value of x^2 + 1 / x^2 is 27.

Step-by-step explanation:

= > x^2 - 5x - 1 = 0

Dividing RHS & LHS by x :

= > ( x^2 - 5x - 1 ) / x = 0

= > ( x ^2 / x ) - ( 5x / x ) - ( 1 / x ) = 0

= > x - 5 - ( 1 / x ) = 0

= > x - 1 / x = 5

Square on both sides :

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

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

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

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

= > x^2 + 1 / x^2 = 25 + 2 = 27

Hence the required value of x^2 + 1 / x^2 is 27.