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Euc20191/Sub-Problem 3

Revision as of 11:39, 13 October 2025 by Yuhao2012 (talk | contribs) (Created page with "==Problem== If <math>\frac{1}{x^2}-\frac{1}{x}=2</math>, determine all possible values of <math>x</math>. ==Solution== Let's start by multiplying both sides by <math>x^2</mat...")
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Problem

If $\frac{1}{x^2}-\frac{1}{x}=2$, determine all possible values of $x$.

Solution

Let's start by multiplying both sides by $x^2$. Then, we have $1-x=2x^2$, so $2x^2+x-1=0$, and after applying the quadratic formula, we will get $\boxed{x=-1}$ or $\boxed{x=\frac12}$.

~Yuhao2012

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