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

Toán Lớp 8: tìm x nha (x+1)(x+2)(x+3)(x+4)=24

Toán Lớp 8: tìm x nha
(x+1)(x+2)(x+3)(x+4)=24

Comments ( 1 )

  1. Bạn tham khảo nhé.
    (x+1)(x+2)(x+3)(x+4)=24
    <=>(x+1)(x+4)(x+2)(x+3)=24
    <=>(x^2+4x+x+4)(x^2+3x+2x+6)=24
    <=>(x^2+5x+4)(x^2+5x+6)-24=0     (1)
    \text{Đặt} x^2+5x+5=a
    \text{Phương trình} (1) \text{viết lại:}
    <=>(a+1)(a-1)-24=0
    <=>a^2-1^2-24=0
    <=>a^2-1-24=0
    <=>a^2-25=0
    <=>a^2-5^2=0
    <=>(a-5)(a+5)=0
    =>(x^2+5x+5-5)(x^2+5x+5+5)=0
    <=>(x^2+5x)(x^2+5x+10)=0
    <=>x(x+5)(x^2+2.x. 5/2+25/4+15/4)=0
    <=>x(x+5)[(x+5/2)^2+15/4]=0
    <=>$\left[\begin{matrix} x=0 \\ x+5=0 \\ (x+\dfrac{5}{2})^2+\dfrac{15}{4}=0\end{matrix}\right.$
    <=>$\left[\begin{matrix} x=0 \\ x=-5 \\ (x+\dfrac{5}{2})^2=-\dfrac{15}{4}(\text{Vô lý})\end{matrix}\right.$
    Vậy x\in{0;-5}
     

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

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