Question

if x = 3 - 2√2 , find x² + 1/x²​

Answer 1

x = 3 - 2√2 ----( 1 )

1/x = 1/( 3 - 2√2 )

= ( 3 + 2√2 ) / [1/x = 1/( 3 - 2√2

= ( 3 + 2√2 ) / [ 3² - ( 2√2 )² ]

= ( 3 + 2√2 ) / ( 9 - 8 )

= 3 + 2√2 ----( 2 )

x + 1/x = 3 - 2√2 + 3 + 2√2

= 6 ------( 3 )

x - 1/x = 3 - 2√2 - ( 3 + 2√2 )

= 3 - 2√2 - 3 - 2√2

= - 4√2 ---- ( 4 )

Now ,

x² - 1/x² = ( x + 1/x ) ( x - 1/x )

= 6 × ( - 4√2 )

[ From ( 3 ) and ( 4 ) ]

= - 24√2

HOPE IT HELPS