Question

. If x² +1/
2
= 7, find the values of :
(i) x-1/x
() x +1/x
(ii) 3x ²-3/x²​

Answer 1

I think question is like this

If , x² + 1 / x² = 7 , then find the values,

(1) x - 1 / x

(2) x + 1/x

(3) 3x² - 3 / x²

Solution---> ATQ, x² + 1 / x² = 2

We have an identity

( a - b )² = a² + b² - 2ab , using it we get

(1) ( x - 1 / x )² = ( x )² + ( 1 / x )² - 2 ( x ) ( 1 / x )

= x ² + 1 / x² - 2

= ( x² + 1 / x² ) - 2

= ( 7 ) - 2

( x - 1 / x )² = 5

x - 1 / x = √5

(2) We have an identity,

( a + b )² = a² + b² + 2ab , using it , we get

( x + 1 / x )² = ( x )² + ( 1 / x )² + 2 ( x ) ( 1 / x )

= x² + 1 / x² + 2

= ( x² + 1 / x² ) +2

= ( 7 ) + 2

( x + 1 / x )² = 9

x + 1 / x = 3

(3) 3 x² - 3 / x² = 3 ( x² - 1 / x² )

= 3 { ( x )² - ( 1 / x )² }

We have an identity ,

a² - b² = ( a + b ) ( a - b ) , applying it here we get

= 3 ( x + 1 / x ) ( x - 1 / x )

Putting value of ( x + 1 / x ) and ( x - 1/ x ) , we get

= 3 ( 3 ) ( √5 )

3 x² - 3 / x² = 9 √5