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Problem #828

Bất phương trình

Added by tanthinh about 2 years ago. Updated over 1 year ago.

Status: Closed Start Date: 19-01-2011
Priority: Normal Due date:
Assigned to: tanphu % Done:

100%

Category: Bất phương trình
Target version: -
Votes: 0/0

Description

giải bpt sau:
1/(x+5)+1/(2x-5)<1/(x-4)+1/(2x+4)

History

Updated by tanphu about 2 years ago

    \(\dfrac{1}{x+5}+\dfrac{1}{2x-5} \(\Leftrightarrow \dfrac{3x}{(x+5)(2x-5)}\(\Leftrightarrow 3x\left[\dfrac{1}{(x+5)(2x-5)}-\dfrac{1}{(x-4)(2x+4)}\right] <0 \)
    \(\Leftrightarrow \dfrac{3x(-9x+9)}{(x+5)(2x-5)(x-4)(2x+4)}<0\)

    Lập bảng xét dấu vế trái và cuối cùng được tập nghiệm là:
    \(S=(-\infty;-5) \cup (-2;0) \cup (1;\frac{5}{2}) \cup (4;+\infty)\)

    Updated by tanthinh about 2 years ago

      tanthinh wrote:

      giải bdt sau: 1/(x+5)+1/(2x-5)<1/(x-4)+1/(2x+4)

      2/ (x^2-4x+1)^2>(x^2+2x+1)

      Updated by tanthinh about 2 years ago

        3/ (x^2-16x+21)

        Updated by tanphu over 1 year ago

        • Subject changed from Bất đẳng thức to Bất phương trình

        Updated by tanphu over 1 year ago

        • Project changed from Tấn Thịnh to Math Learning

        Updated by tanphu over 1 year ago

        • Category set to Bất phương trình
        • Status changed from New to Closed
        • Assigned to set to tanphu
        • % Done changed from 0 to 100