Question

If x square +1/x square=7 find 3x square-3/x square

Answer 1

Answer:

9√5

Step-by-step explanation:

Given-----> x² + 1 / x² = 7

To find ------> 3x² - 3 / x²

Solution-------> We know that,

1) ( a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab

3) ( a² - b² ) = ( a + b ) ( a - b )

ATQ, ( x² + 1 / x² ) = 7

Now, Applying first identity

( x + 1 / x )² = x² + 1 / x² + 2 ( x ) ( 1 / x )

= ( x² + 1 / x² ) + 2

= ( 7 ) + 2

= 9

=> ( x + 1 / x ) = 3

Now, applying second identity

( x - 1 / x )² = x² + 1 / x² - 2 ( x ) ( 1 / x )

= ( x² + 1 / x² ) - 2

= ( 7 ) - 2

=> ( x - 1 / x )² = 5

=> ( x - 1 / x ) = √5

Now,

3 x² - 3 / x² = 3 ( x² - 1 / x² )

= 3 { ( x )² - ( 1 / x )² }

Applying third identity , we get,

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

= 3 ( 3 ) ( √5 )

= 9 √5