(x-3) /2014 + (x-2) /2015 – (x-1) /2016 = -3

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(x-3) /2014 + (x-2) /2015 – (x-1) /2016 = -3

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Aaliyah 6 ngày 2021-09-15T07:58:23+00:00 1 Answers 0 views 0

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    2021-09-15T07:59:32+00:00

    $\frac{x-3}{2004} + \frac{x-2}{2005} – \frac{x-1}{2006} = 3$   $\text{Chỗ kia phải là 3}$

    $⇔\frac{x-3}{2004} + \frac{x-2}{2005} – \frac{x-1}{2006} -3= 0$

    $⇔\frac{x-3}{2004} -1+ \frac{x-2}{2005} -1 – \frac{x-1}{2006} -1= 0$

    $⇔\frac{x-3}{2004} -\frac{2004}{2004}+ \frac{x-2}{2005} -\frac{2005}{2005} – \frac{x-1}{2006} -\frac{2006}{2006}= 0$

    $⇔\frac{x-2007}{2004} + \frac{x-2007}{2005}  – \frac{x-2007}{2006} = 0$

    $⇔(x-2007)(\frac{1}{2004} + \frac{1}{2005}  – \frac{1}{2006} )= 0$

    $⇒x-2007= 0$ $\text{vì}$ $(\frac{1}{2004} + \frac{1}{2005}  – \frac{1}{2006} \neq0)$

    $⇒x=0+2007=2007.$

    $\text{Vậy x=2007.}$.

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