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

Toán Lớp 8: 1.phân tích đa thức thành nhân tử: a^4-b^2(2a-b)^2 2. tìm X biết: a. (5x-4)^2-49x^2=0 b.(6x+1)^2-(x+1)^2=0 tlhn, 5vt, cảm ơn

Tháng Hai 11, 2023 Toán học 2 Comments 0 views

Toán Lớp 8: 1.phân tích đa thức thành nhân tử: a^4-b^2(2a-b)^2
2. tìm X biết:
a. (5x-4)^2-49x^2=0
b.(6x+1)^2-(x+1)^2=0
tlhn, 5vt, cảm ơn

Comments ( 2 )

  1. buithaianh98
    buithaianh98
    11 Tháng Hai, 2023 at 3:57 chiều
    Reply
    1. a^4-b^2(2a-b)^2
    =a^4-[b(2a-b)]^2
    =a^4-(2ab-b^2)^2
    =(a^2-2ab+b^2)(a^2+2ab-b^2)
    =(a-b)^2(a^2+2ab-b^2)
    2.
    a) (5x-4)^2-49x^2=0
    ⇔(5x-4-7x)(5x-4+7x)=0
    ⇔(-2x-4)(12x-4)=0
    ⇔\(\left[ \begin{array}{l}-2x-4=0\\12x-4=0\end{array} \right.\) 
    ⇔\(\left[ \begin{array}{l}x=-2\\x=1/3\end{array} \right.\) 
    b) (6x+1)^2-(x+1)^2=0
    ⇔(6x+1+x+1)(6x+1-x-1)=0
    ⇔(7x+2)5x=0
    ⇔\(\left[ \begin{array}{l}7x+2=0\\5x=0\end{array} \right.\) 
    ⇔\(\left[ \begin{array}{l}x=-2/7\\x=0\end{array} \right.\) 

  2. thienthanh
    thienthanh
    11 Tháng Hai, 2023 at 3:57 chiều
    Reply
    Giải đáp:
    $\\$
    1,
    a^4 – b^2 (2a-b)^2
    = a^4 – [b^2 (2a-b)^2]
    = a^4 – [b (2a-b)]^2
    = a^4 – [2ab – b^2]^2
    = (a^2)^2 – [2ab – b^2]^2
    = [a^2 – (2ab – b^2)] [a^2 + (2ab – b^2)]
    = [a^2 – 2ab + b^2] [a^2 + 2ab – b^2]
    = (a-b)^2 [a^2 + 2ab – b^2]
    $\\$
    2,
    a,
    (5x-4)^2 – 49x^2 = 0
    ↔ (5x-4)^2 – (7x)^2=0
    ↔ [(5x-4)-7x] [(5x-4)+7x]=0
    ↔ [5x-4-7x][5x-4+7x]=0
    ↔ [-2x-4] [12x – 4]=0
    ↔ \(\left[ \begin{array}{l}-2x-4=0\\12x-4=0\end{array} \right.\) 
    ↔ \(\left[ \begin{array}{l}-2x=4\\12x=4\end{array} \right.\) 
    ↔ \(\left[ \begin{array}{l}x=-2\\x=\dfrac{1}{3}\end{array} \right.\) 
    Vậy S= {-2;1/3}
    b,
    (6x+1)^2 – (x+1)^2=0
    ↔ [(6x+1) – (x+1)] [(6x+1) + (x+1)]=0
    ↔ [6x+1-x-1] [6x+1+x+1]=0
    ↔ [(6x-x)+(1-1)] [(6x+x) + (1+1)]=0
    ↔ 5x [7x+2]=0
    ↔ \(\left[ \begin{array}{l}5x=0\\7x+2=0\end{array} \right.\) 
    ↔ \(\left[ \begin{array}{l}x=0\\7x=-2\end{array} \right.\) 
    ↔ \(\left[ \begin{array}{l}x=0\\x=\dfrac{-2}{7}\end{array} \right.\) 
    Vậy S = {0; (-2)/7}

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

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