Question

if y=3-2root2, evaluate (y-1/y)^2

Answer 1

Hi ,

y = 3 - 2√2----( 1 )

1/y = 1 / ( 3 - 2√2 )

rationalize the denominator,

1 / y = ( 3 + 2√2 ) / [ ( 3 - 2√2 )(3 + 2√2 )]

= ( 3 + 2√2 ) / [ 3² - ( 2√2 )]

= ( 3 + 2√2 ) / ( 9 - 8 )

= 3 + 2√2 ----( 2 )

( y - 1/ y )² = [ 3 - 2√2 - ( 3 + 2√2 ) ]²

= ( 3 - 2√2 - 3 - 2√2 )²

= ( - 4√2 )²

= 32

I hope this helps you.

:)