Toán Tìm x, biết: | x+ 1/3| + |x + 4/3| = 9/2 x 04/07/2021 By Ruby Tìm x, biết: | x+ 1/3| + |x + 4/3| = 9/2 x
Đáp án + Giải thích các bước giải: Với `∀x` có: `|x+1/3|\ge0;|x+4/3|\ge0` `=>|x+1/3|+|x+4/3|\ge0` `=>9/2x\ge0` `=>x\ge0` `=>x+1/3>0;x+4/3>0` `|x+1/3|+|x+4/3|=9/2x` `=>x+1/3+x+4/3-9/2x=0` `=>(x+x-9/2x)+(1/3+4/3)=0` `=>-5/2x+5/3=0` `=>-5/2x=-5/3` `=>x=2/3` Trả lời
Ta có: `| x+ 1/3| + |x + 4/3|≥ |x+ 1/3 + x + 4/3|` Dấu `=` xảy ra khi: `|x+ 1/3 + x + 4/3| = 9/2x` `2x + 5/3 = 9/2x` `2x + 5/3 – 5/3 = (9x)/2 – 5/3` `2x = (9x)/2 – (2(-5/3))/2` `2x = (9x + 2(-5/3))/2` `2x = (9x – 10/3)/2` `2.2x = 2.(9x – 10/3)/2` `4x = 9x – 10/3` `4x – 9x = 9x – 10/3 – 9x` `-5x = -10/3` `(-5x)/(-5) = (-10/3)/(-5)` `⇒x = 2/3` Trả lời
Đáp án + Giải thích các bước giải:
Với `∀x` có: `|x+1/3|\ge0;|x+4/3|\ge0`
`=>|x+1/3|+|x+4/3|\ge0`
`=>9/2x\ge0`
`=>x\ge0`
`=>x+1/3>0;x+4/3>0`
`|x+1/3|+|x+4/3|=9/2x`
`=>x+1/3+x+4/3-9/2x=0`
`=>(x+x-9/2x)+(1/3+4/3)=0`
`=>-5/2x+5/3=0`
`=>-5/2x=-5/3`
`=>x=2/3`
Ta có: `| x+ 1/3| + |x + 4/3|≥ |x+ 1/3 + x + 4/3|`
Dấu `=` xảy ra khi: `|x+ 1/3 + x + 4/3| = 9/2x`
`2x + 5/3 = 9/2x`
`2x + 5/3 – 5/3 = (9x)/2 – 5/3`
`2x = (9x)/2 – (2(-5/3))/2`
`2x = (9x + 2(-5/3))/2`
`2x = (9x – 10/3)/2`
`2.2x = 2.(9x – 10/3)/2`
`4x = 9x – 10/3`
`4x – 9x = 9x – 10/3 – 9x`
`-5x = -10/3`
`(-5x)/(-5) = (-10/3)/(-5)`
`⇒x = 2/3`