Question

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

Answer 1

34

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