# Thread: Something wrong with my working.

1. ## Something wrong with my working.

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

2. Hello my friend

Originally Posted by Joel
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
This is correct!

Originally Posted by Joel
(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
No, Thus $\displaystyle x^2+2 + \frac{1}{x^2} = 9$
So

$\displaystyle x^2+\frac{1}{x^2} = 9 - 2$
Hence

$\displaystyle x^2+\frac{1}{x^2} = 7$

Yours
Rapha

3. If x + ⅟x = 3

( x + ⅟x )² = (3)²

From (a)

x² + 2 + ⅟x₂ = (3)²
x² + 2 + ⅟x₂ = 9

Subtract 2 from both sides

x² + ⅟x₂ = 7