If x = 3-2√2 ,then find the value of x2 – 1/x2

Hello there!

x^2 - (1/x^2)

x = 3 - 2√2 -- (1)

1/x = 1/( 3-2√2 )

= ( 3 + 2√2 ) / (3 - 2√2 )(3+2√2 )

= ( 3 + 2√2 ) / 3² - ( 2√2 )²

3^2 = 9 and 2√2 ² = 8

= ( 3 + 2√2 ) / ( 9 - 8 )

= ( 3 + 2√2) -- (2)

x - 1/x = 3 - 2√2 - ( 3 + 2√2 )

= 6

= 3 - 2√2 - 3 - 2√2

= - 4√2

x² - 1/x² = ( x + 1/x ) ( x - 1/x )

= 6 × ( - 4√2 )

6 x ( -4√2 ) = -24√2