Question

Giải phương trình sau: \(\frac{x}{2012}+\frac{x+1}{2013}+\frac{x+2}{2014}+\frac{x+3}{2015}+\frac{x+4}{2016}=5\)

Giải phương trình sau : \(\frac{x-90}{10}\)+ \(\frac{x-76}{12}\) +\(\frac{x-58}{14}\) + \(\frac{x-36}{16}\) +\(\frac{x-15}{17}\) \(=15\)

Answer 1

1. \(\frac{x}{2012}+\frac{x+1}{2013}+\frac{x+2}{2014}+\frac{x+3}{2015}+\frac{x+4}{2016}=5\)

<=>\(\left(\frac{x}{2012}-1\right)\)+\(\left(\frac{x+1}{2013}-1\right)\)+ \(\left(\frac{x+2}{2014}-1\right)\)+\(\left(\frac{x+3}{2015}-1\right)\)+ \(\left(\frac{x+4}{2016}-1\right)\)=0

<=> \(\frac{x-2012}{2012}+\frac{x-2012}{2013}+\frac{x-2012}{2014}+\frac{x-2012}{2015}+\frac{x-2012}{2016}\)=0

<=> (x-2012)(\(\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}+\frac{1}{2016}\)) = 0

<=> x-2012 = 0 ( vì \(\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}+\frac{1}{2016}\ne0\))

<=> x = 2012

Answer 2

2. \(\frac{x-90}{10}+\frac{x-76}{12}\)+ \(\frac{x-58}{14}+\frac{x-36}{16}\)+ \(\frac{x-15}{17}=15\)

<=> \(\left(\frac{x-90}{10}-1\right)\)+ \(\left(\frac{x-76}{12}-2\right)\)+ \(\left(\frac{x-58}{14}-3\right)\)+ \(\left(\frac{x-36}{16}-4\right)\)+ \(\left(\frac{x-15}{17}-5\right)\)= 0

<=> \(\frac{x-100}{10}+\frac{x-100}{12}+\frac{x-100}{14}+\frac{x-100}{16}+\frac{x-100}{17}\)=0

<=> (x-100) =0 (vì \(\frac{1}{10}+\frac{1}{12}+\frac{1}{14}+\frac{1}{16}+\frac{1}{17}\ne0\))

<=> x= 100