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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: Chưng minh luôn âm với mọi x 1. -x^2+x-1 2. -x^2+3x-3

Toán Lớp 8: Chưng minh luôn âm với mọi x
1. -x^2+x-1
2. -x^2+3x-3

Comments ( 2 )

  1. 1.
    -x^2+x-1
    =-(x^2-x+1)
    =-(x^2-2.x.(1)/2+1/4+3/4)
    =-[(x-1/2)^2+3/4]
    Ta có: [(x-1/2)^2+3/4]>0 AA x
    =>-[(x-1/2)^2+3/4]<0 AA x
    Vậy -x^2+x-1 luôn âm với mọi x
    2.
    -x^2+3x-3
    =-(x^2-3x+3)
    =-(x^2-2.x.(3)/2+4/9+3/4)
    =-[(x-3/2)^2+3/4]
    Ta có: [(x-3/2)^2+3/4]>0 AA x
    =>-[(x-3/2)^2+3/4]<0 AA x
    Vậy -x^2+3x-3 luôn âm với mọi x
    Xin hay nhất cho nhóm ạ

  2. -x^2+x-1
    =-x^2+x-1/4+1/4-1
    =-(x^2-x+1/4)+1/4-1
    =-(x-1/2)^2-3/4≤-3/4<0∀x (đpcm)
    ________________________________________________
    -x^2+3x-3
    =-x^2+3x-9/4+9/4-3
    =-(x^2-3x+9/4)+9/4-3
    =-(x-3/2)^2-3/4≤-3/4<0∀x (đpcm)

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222-9+11+12:2*14+14 = ? ( )