Question

if x=3-2√2, find the value of x²-1/x²

Answer 1

Hi ,

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√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

I hope this helps you.

: )

Answer 2

1/x=3+2√2
x-1/x=3-2√2-3-2√2=-4√2
x^2-1/x^2=(-4√2)^2+2=32+2=34
hooe this is the answer