Euc20191/Sub-Problem 3

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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Euc20191/Sub-Problem 3

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