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

Toán Lớp 7: Cho `(x-1)/2=(y-2)/3=(z-3)/4` và `2x-3y+5z=56` Tìm `x; y; z`

Toán Lớp 7: Cho (x-1)/2=(y-2)/3=(z-3)/4 và 2x-3y+5z=56
Tìm x; y; z

Comments ( 2 )

  1. Trả lời:
    (2(x-1)-3(y-2)+5(z-3))/(2.2-3.3+5.4)
    =(2x-2-3y+6+5z-15)/(4-9+20)
    =((2x-3y+5z)-(2-6+15))/15
    =(56-11)/15
    =45/15
    =3
    $\text{Suy ra:}$
    (x-1)/2=3=>x-1=6=>x=7
    (y-2)/3=3=>y-2=9=>y=11
    (z-3)/4=3=>z-3=12=>z=15
    $\text{Vậy}$ (x;y;z)=(7;11;15)

  2. Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
    \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}
    =\frac{2.(x-1)-3.(y-2)+5.(z-3)}{2.2-3.3+5.4}
    =\frac{2.x-2.1-3.y+3.2+5.z-5.3}{4-9+20}
    =\frac{2x-2-3y+6+5z-15}{15}
    =\frac{2x-3y+5z-2+6-15}{15}
    =\frac{2x-3y+5z-11}{15}
    =\frac{56-11}{15}
    =\frac{45}{15}
    =3
    $\\$
    Do đó:
    @\frac{x-1}{2}=3=>x=3.2+1=>x=7
    @\frac{y-2}{3}=3=>y=3.3+2=>y=11
    @\frac{z-3}{4}=3=>z=4.3+3=>z=15
    Vậy x=7; y=11; z=15

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