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

Toán Lớp 9: Giải pt: `[3(x+1)-2(x+3)]^3+[2(x+3)-x+5]^3+[x-5-3(x+1)^3]=0`

Tháng Chín 3, 2022 Toán học 2 Comments 0 views

Toán Lớp 9: Giải pt:
[3(x+1)-2(x+3)]^3+[2(x+3)-x+5]^3+[x-5-3(x+1)^3]=0

Comments ( 2 )

  1. kimoanh34
    kimoanh34
    3 Tháng Chín, 2022 at 12:36 chiều
    Reply
    [3(x+1)-2(x+3)]^3+[2(x+3)-x+5]^3+[x-5-3(x+1)]^3=0
    Đặt {(3(x+1)=a),(2(x-3)=b),(x-5=c):}
    =>(a-b)^3+(b-c)^3+(c-a)^3=0\ (2)
    Vì a-b+b-c+c-a=0
    =>(a-b)^3+(b-c)^3+(c-a)^3=3(a-b)(b-c)(c-a)\ (3)
    Từ (2) và (3)=>3(a-b)(b-c)(c-a)=0
    =>\(\left[ \begin{array}{l}a-b=0\\b-c=0\\c-a=0\end{array} \right.\) 
    =>\(\left[ \begin{array}{l}a=b\\b=c\\c=a\end{array} \right.\) 
    =>\(\left[ \begin{array}{l}3(x+1)=1(x-3)\\2(x+3)=x-5\\x-5=3(x+1)\end{array} \right.\) 
    =>\(\left[ \begin{array}{l}3x+3=2x-6\\2x+6=x-5\\x-5=3x+3\end{array} \right.\) 
    =>\(\left[ \begin{array}{l}3x-2x=-3-6\\2x-x=-6-5\\x-3x=5+3\end{array} \right.\) 
    =>\(\left[ \begin{array}{l}x=-9\\x=-11\\x=-4\end{array} \right.\) 
    Vậy S={-9;-11;-4}

  2. ngocle44
    ngocle44
    3 Tháng Chín, 2022 at 12:36 chiều
    Reply
    [3(x+1)-2(x+3)]^3+[2(x+3)-x+5]^3+[x-5-3(x+1)]^3=0
    Đặt: 3(x+1)=a
            2(x+3)=b
             x-5=c
    <=>(a-b)^3+(b-c)^3+(c-a)^3=0
    <=>a^3-3a^2b+3ab^2-b^3+b^3-3b^2c+3bc^2-c^3+c^3-3c^2a+3ca^2-a^3=0
    <=>-3a^2b+3ab^2-3b^2c+3bc^2-3c^2a+3ca^2=0
    <=>-3(a^2b-ab^2+b^2c-bc^2+c^2a-ca^2)=0
    <=>abc-a^2b-ac^2+a^2c-b^2c+b^2a+bc^2-abc=0
    <=>a(bc-ab-c^2+ca)-b(bc-ab-c^2+ca)=0
    <=>(a-b)(bc-ab-c^2+ca)=0
    <=>(a-b)[b(c-a)-c(c-a)]=0
    =>(a-b)(b-c)(c-a)=0
    <=>[(a-b=0),(b-c=0),(c-a=0):}
    <=>[(3x+3-2x-6=0),(2x+6-x+5=0),(x-5-3x-3=0):}
    <=>[(x=3),(x=-11),(-2x=8):}
    <=>[(x=3),(x=-11),(x=-4):}
    Vậy S={3;-11;4}

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

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