Question

if x is equal to 3 + under root 8 and Y is equal to 3 minus under root 8 then 1 divided by X square + 1 / y square =

Answer 1

Hi ,

x = 3 + √8

1/x = 1/( 3 + √8 )

= [ ( 3 - √8 )/(3+√8 )( 3 - √8 )]

= ( 3 - √8 )/[ 3² - ( √8 )² ]

= ( 3 - √8 )/ ( 9 - 8 )

= 3 - √8 ---( 1 )

Similarly ,

ii ) y = 3 - √8

1/y = 3 + √8 ---( 2 )

Now ,

1/x² + 1/y²

= ( 3 - √8 )² + ( 3 + √8 )²

= 2 [ 3² + ( √8 )² ]

= 2 ( 9 + 8 )

= 2 × 17

= 34

I hope this helps you.

: )

Answer 2

x = 3+√8

1/x = 3+√8

By rationalization, 1/x = (3-√8)/[3²-(√8)²]

1/x = (3-√8)/(9-8) = (3-√8)/1 = 3-√8

1/x² = (3-√8)² = 9+8-6√8 = 17-√8

====================

y = 3-√8

1/y = 1/(3-√8)

By rationalization, 1/y = (3+√8)/[3²-(√8)]

1/y = (3+√8)/(9-8) = 3+√8

1/y² = (3+√8)² = 9+8+6√8 = 17+6√8

.
Then,

1/x² + 1/y²

17-6√8 + 17+6√8

34



I hope this will help you


-by ABHAY