Question

if x=3+√8 and y=3-√8 then 1/x^2+1/y^2=

Answer 1

Hello Mate!

x = 3 + root 8
1/x = 1/ ( 3 + root 8 ) × ( 3 - root 8 )/ ( 3 - root 8 )
= ( 3 + root 8 ) / ( 9 - 8 )
= 3 + root 8

y = 3 - root 8
1/ y = 1/ ( 3 - root 8 ) × ( 3 + root 8 ) / ( 3 + root 8 )
= 3 + root 8

1/x^2 = ( 3 - root 8 )^2
9 + 8 - 6 root 8
= 17 - 6 root 8

1/y^2 = ( 3 + root 8 )^2
= 17 + 6 root 8

Arrange,

17 - 6 root 8 + 17 + 6 root 8
= 34

Hope it helps☺!✌