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# Completing the square

Maths and statistics discussion, revision, exam and homework help.

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1. Completing the square
Does anyone know the steps to get from:

x2 -2 + 1/x2 > 0

To this:

(x - 1/x)2 > 0

I assume it is completing the square but it could not be.
2. Re: Completing the square
2 = 2x*(1/x)

So x^2 - 2 + 1/x^2 = x^2 - 2x*(1/x) + 1/x^2

See if you can do it from there
3. Re: Completing the square
(Original post by oh_1993)
2 = 2x*(1/x)

So x^2 - 2 + 1/x^2 = x^2 - 2x*(1/x) + 1/x^2

See if you can do it from there
still can't sorry. How did you get to 2 = 2x*(1/x)
4. Re: Completing the square
(x - 1/x)^2

Expand this and see what you get
5. Re: Completing the square
(Original post by 2710)
(x - 1/x)^2

Expand this and see what you get
The original equation:

x^2 -2 + 1/x^2
6. Re: Completing the square
(Original post by CF25)
still can't sorry. How did you get to 2 = 2x*(1/x)
(1/x)*x=1
hence
2=2x*(1/x)

I'll give you a hint on how to continue:

(a+b)^2=a^2+2ab+b^2
7. Re: Completing the square
(Original post by CF25)
The original equation:

x^2 -2 + 1/x^2
Yes, so it is just by inspection how you get from one to the other
8. Re: Completing the square
It is the equivalent of knowing that

9. Re: Completing the square
Thanks guys, got it.
10. Re: Completing the square
Looking at that, I would probably just do it by inspection..

However, you could also try multiplying through by x^2, and then let x^2=X, and rearrange as if it was a normal quadratic, if that's easier. You'll need to substitute back in at the end, though.

Edit: Oops, looks like you've solved it while I was posting.. never mind

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Last updated: April 16, 2012
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