Giải ptrình 3-x/2013 – 1 = 2-x/2014 – x/2016 31/10/2021 Bởi Alice Giải ptrình 3-x/2013 – 1 = 2-x/2014 – x/2016
Đáp án: ` x=2016` Giải thích các bước giải: ` \frac{3-x}{2013}-1=\frac{2-x}{2014}-\frac{x}{2016}` `⇒\frac{3-x}{2013}-1-\frac{2-x}{2014}+\frac{x}{2016}=0` `⇒(\frac{3-x}{2013}-1+2)-(\frac{2-x}{2014}+1)+(\frac{x}{2016}+1)=0` `⇒\frac{2016-x}{2013}-\frac{2016-x}{2014}+\frac{2016+x}{2016}=0` `⇒(2016-x)(\frac{1}{2013}-\frac{1}{2014}+\frac{1}{2016}=0` `⇔2016-x=0` `⇒x=2016` Bình luận
`{3-x}/2013 – 1 = {2-x}/2014 – x/2016``\Leftrightarrow {3-x}/2013 – 1 + 2= {2-x}/2014 + (-x/2016) +2``\Leftrightarrow {3-x}/2013 + 1 = ({2-x}/2014+1) + (-x/2016+1)``\Leftrightarrow {2016 – x}/2013 = {2016 – x}/2014 + {2016 – x}/2016``\Leftrightarrow {2016 – x}/2013 – {2016 – x}/2014 – {2016 – x}/2016=0``\Leftrightarrow ( 2016 – x )( {1}/2013 – {1}/2014 – {1}/2016 )=0`( Vì ` {1}/2013 – {1}/2014 – {1}/2016 \ne 0` )`\Leftrightarrow 2016 – x = 0``\Leftrightarrow x = 2016`Vậy `S = { 2016 }` Bình luận
Đáp án:
` x=2016`
Giải thích các bước giải:
` \frac{3-x}{2013}-1=\frac{2-x}{2014}-\frac{x}{2016}`
`⇒\frac{3-x}{2013}-1-\frac{2-x}{2014}+\frac{x}{2016}=0`
`⇒(\frac{3-x}{2013}-1+2)-(\frac{2-x}{2014}+1)+(\frac{x}{2016}+1)=0`
`⇒\frac{2016-x}{2013}-\frac{2016-x}{2014}+\frac{2016+x}{2016}=0`
`⇒(2016-x)(\frac{1}{2013}-\frac{1}{2014}+\frac{1}{2016}=0`
`⇔2016-x=0`
`⇒x=2016`
`{3-x}/2013 – 1 = {2-x}/2014 – x/2016`
`\Leftrightarrow {3-x}/2013 – 1 + 2= {2-x}/2014 + (-x/2016) +2`
`\Leftrightarrow {3-x}/2013 + 1 = ({2-x}/2014+1) + (-x/2016+1)`
`\Leftrightarrow {2016 – x}/2013 = {2016 – x}/2014 + {2016 – x}/2016`
`\Leftrightarrow {2016 – x}/2013 – {2016 – x}/2014 – {2016 – x}/2016=0`
`\Leftrightarrow ( 2016 – x )( {1}/2013 – {1}/2014 – {1}/2016 )=0`
( Vì ` {1}/2013 – {1}/2014 – {1}/2016 \ne 0` )
`\Leftrightarrow 2016 – x = 0`
`\Leftrightarrow x = 2016`
Vậy `S = { 2016 }`