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Question

Tìm x, y, z $\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$và 2x+3y-2=50

Cherry Võ · Accepted Answer

bn ơi , bn ghi đề sai akCâu trả lời: bn ơi , bn ghi đề sai ak

Lưu Hạ Vy · Answer

Đặt $\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}=m$

$\Rightarrow x=2m+1;y=3m+2;z=4m+3$

mà $2x+3y-z=50$

$\Rightarrow2.\left(2m+1\right)+3.\left(3m+2\right)-\left(4m+3\right)=50$

$\Rightarrow4m+2+9m+6-4m-3=50$

$\Rightarrow4m+9m-4m+2+6-3=50$

$\Rightarrow9m+5=50$

$\Rightarrow9m=45\Rightarrow m=5$

Với $m=5$

$\Rightarrow$ $x=2.5+1=11$

$y=3.5+2=17$

$z=4.5+3=23$

Vậy ....Câu trả lời: Đặt $\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}=m$

$\Rightarrow x=2m+1;y=3m+2;z=4m+3$

mà $2x+3y-z=50$

$\Rightarrow2.\left(2m+1\right)+3.\left(3m+2\right)-\left(4m+3\right)=50$

$\Rightarrow4m+2+9m+6-4m-3=50$

$\Rightarrow4m+9m-4m+2+6-3=50$

$\Rightarrow9m+5=50$

$\Rightarrow9m=45\Rightarrow m=5$

Với $m=5$

$\Rightarrow$ $x=2.5+1=11$

$y=3.5+2=17$

$z=4.5+3=23$

Vậy ....

Cherry Võ · Answer

$\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$

$\Rightarrow\dfrac{2x-2}{4}=\dfrac{3y-6}{9}=\dfrac{z-3}{4}=\dfrac{\left(2x-2\right)+\left(3y-6\right)-\left(z-3\right)}{4+9-4}$

=$\dfrac{\left(2x+3y-z\right)-2-6+3}{9}=\dfrac{45}{9}=5$

$\Rightarrow\dfrac{x-1}{2}=5\Rightarrow x=11$

$\Rightarrow\dfrac{y-2}{3}=5\Rightarrow y=17$

$\Rightarrow\dfrac{z-3}{4}=5\Rightarrow z=23$Câu trả lời: $\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$

$\Rightarrow\dfrac{2x-2}{4}=\dfrac{3y-6}{9}=\dfrac{z-3}{4}=\dfrac{\left(2x-2\right)+\left(3y-6\right)-\left(z-3\right)}{4+9-4}$

=$\dfrac{\left(2x+3y-z\right)-2-6+3}{9}=\dfrac{45}{9}=5$

$\Rightarrow\dfrac{x-1}{2}=5\Rightarrow x=11$

$\Rightarrow\dfrac{y-2}{3}=5\Rightarrow y=17$

$\Rightarrow\dfrac{z-3}{4}=5\Rightarrow z=23$

Bài 8: Tính chất của dãy tỉ số bằng nhau