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# algebra

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The difference between a number and its reciprocal is 3.  What are the possible values of the number?

Sep 23, 2020

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The difference between a number and its reciprocal is 3. What are the possible values of the number?

Hello Guest!

$$a-\frac{1}{a}=3\\ \frac{a^2-1}{a}=3\\ a^2-1=3a\\ a^2-3a-1=0$$

$$a=1.5\pm\sqrt{1.5^2+1}$$

$${\color{blue}a_1}=1.5+1.803=\color{blue}3.303\\ {\color{blue}\frac{1}{a_1}}=\color{blue}0.303$$

$${\color{blue}a_2}=1.5-1.803=\color{blue}-0.303\\ {\color{blue}\frac{1}{a_2}}=\color{blue}-3.303$$

!

!

Sep 23, 2020
edited by asinus  Sep 23, 2020
edited by asinus  Sep 23, 2020