Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Sorry, I am not sure how to do the maths mark-up on this site but hopefully the question will make sense. I should know how to do this, but I have got myself stuck! Can anyone help?


share|cite|improve this question
up vote 18 down vote accepted

$$\left(x-\frac{1}{x}\right)^2= \dots?$$

share|cite|improve this answer
Thanks! Took me a moment to figure out what you were on about, but I do see how to simplify it now. So the smallest value I get factorising to get that and then substituting it in should be x-(1/x)... Assuming I understood you correctly, that is... – Magpie Jul 26 '12 at 16:55
+1 for the question mark. – dot dot Jul 26 '12 at 17:03
@Magpie, I'm not sure what you mean by "the smalles value I get factorising...". The fact is your expression $\,x^2-2+x^{-2}\,$ has the expected form for the well-known squared binomial expression: (term 1 squared) + (term 2 squared) $\,\pm\,$ (twice term 1 times term 2) = (term 1 $\,\pm\,$ term 2)^2...practice, that's all. – DonAntonio Jul 26 '12 at 18:36
@DonAntonio Your answer is contradictory to jasoncube's. The expression is factored appropriately, however the initial exponent of $1/2$ should cancel out the exponent of $2$. Am I misunderstanding something? – user26649 Jul 27 '12 at 12:16
@FarhadYusufali, I think you are. I can't see how my answer is "contradictory to jasoncube's". IMO, both are accurate – DonAntonio Jul 27 '12 at 12:50

$$ \sqrt{x^2 + x^{-2} - 2} = \sqrt{x^2 – 2(x)(x^{-1})+ (x^{-1})^2} =\sqrt{(x – x^{-1})^2} = |x – x^{-1}| $$

share|cite|improve this answer

What is $x^{-2}$ equal to? Hint: can you write it as a fraction? If so, I would then look at adding and subtracting fractions and go from there.

share|cite|improve this answer

For $x\ne 0$, $x^2+x^{-2}-2=(x^4-2x^2+1)/x^2=(x^2-1)^2/x^2$. So taking square roots of both sides we get on the right side $|(x^2-1)/x|=|x-1/x|$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.