Question

If x^2+ 1/x^2=7 then find 3x^2-3/x^2

Answer 1

Answer:

9√5

Step-by-step explanation:

We know that

( a - b )² = ( a + b )² - 4ab

=> ( x² - 1/x² )² = ( x² + 1/x² )² - 4( x² )( 1/x² )

=> ( x² - 1/x² )² = 7² - 4

=> ( x² - 1/x² )² = 49 - 4

=> ( x² - 1/x² )² = 45

=> x² - 1/x² = √45 = √9 × √5 = 3√5

3x² - 3/x²

= 3( x² - 1/x² )

= 3( 3√5 )

= 9√5