If x=3+root8 and y = 3 - root 8 find 1/x^2+1/y^2

34

Step-by-step explanation:

x=3+√8

y = 3-√8

now,

1/x^2+1/y^2

=1 / (3+√8) ² + 1 / (3-√8) ²

= [ (3-√8) ² + (3+√8) ²] / (3+√8) ² (3-√8) ² [L. C. M = (3+√8) ² (3-√8) ² ]

=[ (3-√8+3+√8) ²-2 (3-√8) (3+√8) ] / [ (3+√8) (3-√8) ]²

=[6²-2. (3²-√8²) ] / (3²-√8²) ² [ a² + b² = (a+b) ²-2ab]

=[36-2 (9-8) ] / (9-8) ²

=[36-2.1] / 1²

=34