|x+1|+|x+2|+|x+5|=3x

Question

|x+1|+|x+2|+|x+5|=3x

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Edana Edana 4 years 2020-11-20T12:26:44+00:00 2 Answers 76 views 0

Answers ( )

  1. Helga
    0
    2020-11-20T12:27:46+00:00
    Reply

    `|x+1|+|x+2|+|x+5|=3x`

    mà `|x+1|+|x+2|+|x+5|>0∀x`

    `→3x>0`

    `→x>0`

    `→|x+1+|x+2|+|x+5|=x+1+x+2+x+5=3x+8`

    `→3x+8=3x`

    `→8=0` (Vô lý)

    `→x=∅`

     

  2. Jezebel
    0
    2020-11-20T12:27:56+00:00
    Reply

    Ta có: `|x + 1| ≥ 0; |x + 2| ≥ 0; |x + 5| ≥ 0`

    `→ |x + 1| + |x + 2| + |x + 5| ≥ 0`

    `→ 3x ≥ 0`

    `→ x ≥ 0`

    `→ |x + 1| = x + 1; |x + 2| = x + 2; |x + 5| = x + 5`

    `Pt ↔ x + 1 + x + 2 + x + 5 = 3x`

    `↔ 3x + 8 = 3x`

    `↔ 0 = 8` (vô nghiệm)  

     

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