Art of Problem Solving

Euc20191/Sub-Problem 3: Difference between revisions

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Latest revision as of 10:39, 13 October 2025

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