Hi guys,

Have answered this question, but when I checked the final answer it should be 7 not 11. Can you help me with where I went wrong. Cheers.

(a) Expand ( x + ⅟x )² = x² + 2x⅟x + ⅟x₂

= x² + 2 + ⅟x₂

(b) Suppose that x + ⅟x = 3. Use part (a) to evaluate x² + ⅟x² without attempting to find the value of x.

( x + ⅟x )² = x² + 2 + ⅟x₂

If x + ⅟x = 3, then = ( x + ⅟x )²

= ( 3 )²

= 9

Thus x² + 2 + ⅟x₂ = x² + ⅟x₂ + 2

= 9 + 2

So x² + ⅟x₂ = 11