Tìm `x` biết : $\huge\text{|}$`|x-1|+|x-3|`$\huge\text{|}$

Tìm `x` biết :
$\huge\text{|}$`|x-1|+|x-3|`$\huge\text{|}$

0 thoughts on “Tìm `x` biết : $\huge\text{|}$`|x-1|+|x-3|`$\huge\text{|}$”

  1. $\huge\text{|}$`|x-1|+|x-3|`$\huge\text{|}$`=4`

    `⇔ |x-1|+|x-3| = 4`

    TH1 : Nếu `x < 1`, ta có :

    `-(x-1) – (x-3) = 4`

    `⇔ -x + 1 – x + 3 = 4`

    `⇔ -x – x = 4 – 1 – 3`

    `⇔ -2x = 0`

    `⇔ x = 0` $(T/m)$

    TH2 : Nếu `1 ≤ x < 3`, ta có : 

    `(x-1) – (x-3) = 4`

    `⇔ x – 1 – x + 3 = 4`

    `⇔ x – x = 4 + 1 – 3`

    `⇔ 0x = 2` `(KTM)`

    TH3 : Nếu `x ≥ 3`, ta có :

    `(x-1) + (x-3) = 4`

    `⇔ x – 1 + x – 3 = 4`

    `⇔ x + x = 4 + 1 + 3`

    `⇔ 2x = 8`

    `⇔ x = 4` $(T/m)$

    Vậy `x = 0` hoặc `x=4`

    Xin hay nhất !

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