Giúp mk vs các bác ơi ???????????????????????????? October 15, 2020 by Vodka Giúp mk vs các bác ơi ????????????????????????????
`a,` `|x+5|+|3-x|=7` Áp dụng tính chất : `|a|+|b|≥|a+b|` `⇒|x+5|+|3-x|≥|x+5+3-x|=|8|=8` `⇒|x+5|+|3-x|≥8` `(`trái với đề bài`)` $⇒x∈\varnothing$ `b,` `|x+1/2|+|x+1/3|+|x+1/4|+|x+1/5|=5x` `(1)` Vì `|x+1/2|;|x+1/3|;|x+1/4|;|x+1/5|≥0` `∀x` `⇒|x+1/2|+|x+1/3|+|x+1/4|+|x+1/5|≥0` `⇒5x≥0` `⇒x≥0` `⇒x+1/2;x+1/3;x+1/4;x+1/5≥0` `⇒|x+1/2|=x+1/2;|x+1/3|=x+1/3;|x+1/4|=x+1/4;|x+1/5|=x+1/5` Thay vào `(1)` `⇒x+1/2+x+1/3+x+1/4+x+1/5=5x` `⇒4x+77/60=5x` `⇒x=77/60` Reply
`a,` `|x+5|+|3-x|=7`
Áp dụng tính chất : `|a|+|b|≥|a+b|`
`⇒|x+5|+|3-x|≥|x+5+3-x|=|8|=8`
`⇒|x+5|+|3-x|≥8` `(`trái với đề bài`)`
$⇒x∈\varnothing$
`b,` `|x+1/2|+|x+1/3|+|x+1/4|+|x+1/5|=5x` `(1)`
Vì `|x+1/2|;|x+1/3|;|x+1/4|;|x+1/5|≥0` `∀x`
`⇒|x+1/2|+|x+1/3|+|x+1/4|+|x+1/5|≥0`
`⇒5x≥0`
`⇒x≥0`
`⇒x+1/2;x+1/3;x+1/4;x+1/5≥0`
`⇒|x+1/2|=x+1/2;|x+1/3|=x+1/3;|x+1/4|=x+1/4;|x+1/5|=x+1/5`
Thay vào `(1)`
`⇒x+1/2+x+1/3+x+1/4+x+1/5=5x`
`⇒4x+77/60=5x`
`⇒x=77/60`