Toán tìm x thuộc R biết |x+1|+|x+3|+…+|x+2013|=2014x 04/12/2021 By Josephine tìm x thuộc R biết |x+1|+|x+3|+…+|x+2013|=2014x
Có `|x+1|≥0 ` `|x+3|≥0` …. `|x+2013|≥0` `=>`|x+1|+|x+3|+…+|x+2013|≥0` `=>2014x≥0` `=>x≥0` `=>x+2013>x+2011>….>x+3>x+1>x≥0` `=>|x+1|+|x+3|+…+|x+2013|=x+1+x+3+…+x+2013` `=>2014x=1007x+1014049` `=>x=1007` Trả lời
Đáp án: $\text{Ta có: VT>=0 ∀x∈R}$ `=> VP>=0 ∀x∈R` `=> 2014x>=0` `=> x>=0` `=> x+1+x+3+…+x+2013=2014x` `=> 1007x+(2014.2017)/2=2014x` `=> 1007x+1014049=2014x` `=> 1014049=2014x-1007x` `=> 1014049=1007x` `=> x=1007` Trả lời
Có
`|x+1|≥0 `
`|x+3|≥0`
….
`|x+2013|≥0`
`=>`|x+1|+|x+3|+…+|x+2013|≥0`
`=>2014x≥0`
`=>x≥0`
`=>x+2013>x+2011>….>x+3>x+1>x≥0`
`=>|x+1|+|x+3|+…+|x+2013|=x+1+x+3+…+x+2013`
`=>2014x=1007x+1014049`
`=>x=1007`
Đáp án:
$\text{Ta có: VT>=0 ∀x∈R}$
`=> VP>=0 ∀x∈R`
`=> 2014x>=0`
`=> x>=0`
`=> x+1+x+3+…+x+2013=2014x`
`=> 1007x+(2014.2017)/2=2014x`
`=> 1007x+1014049=2014x`
`=> 1014049=2014x-1007x`
`=> 1014049=1007x`
`=> x=1007`