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

Toán Lớp 6: A=(3x-4) ×(7x+8)-1,5x ×(24x+5)-5 ×(1-2x)+1,5x<0 ∀x

Toán Lớp 6: A=(3x-4) ×(7x+8)-1,5x ×(24x+5)-5 ×(1-2x)+1,5x<0 ∀x

Comments ( 2 )

  1. A = (3x – 4)(7x + 8) – 1,5x(24x + 5) – 5(1 – 2x) + 1,5x
    A = 3x(7x + 8) – 4(7x + 8) – 36x^2 – 7,5x – 5 + 10x + 1,5x
    A = 21x^2 + 24x – 28x – 32 – 36x^2 – 7,5x – 5 + 10x + 1,5x
    A = -15x^2 – 37
    Do  x^2 ≥ 0
    ⇒ -15x^2 ≤ 0
    ⇒ A ≤ -37
    text(Vậy A luôn bé hơn 0 với mọi x)

  2. Giải đáp:
    A <0 ∀x
    Lời giải và giải thích chi tiết:
    A = (3x – 4) (7x + 8) – 1,5x  (24x +5) – 5 (1 – 2x) + 1,5x
    -> A = (21x^2 + 24x – 28x – 32) – 36x^2 – 7,5x – 5 + 10x + 1,5x
    -> A = 21x^2 – 4x – 32 – 36x^2 – 7,5x – 5 + 10x + 1,5x
    -> A = (21x^2 – 36x^2) + (-4x – 7,5x + 10x + 1,5x) + (-32 – 5)
    -> A=-15 x^2 – 37
    Với mọi x có : x^2 ≥ 0
    -> -15x^2 ≤0∀x
    -> -15x^2 – 37 ≤ -37 < 0∀x
    -> A < 0∀x 
     

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

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