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\(\dfrac{x}{-4}=\dfrac{y}{-7}=\dfrac{z}{3}=k\Rightarrow\left\{{}\begin{matrix}x=-4k\\y=-7k\\z=3k\end{matrix}\right.\)
\(\Rightarrow A=\dfrac{-2\left(-4k\right)-7k+5.3k}{2.\left(-4k\right)-3.\left(-7k\right)-6.3k}=\dfrac{16k}{-5k}=-\dfrac{16}{5}\)
Đặt \(\dfrac{x}{-4}=\dfrac{y}{-7}=\dfrac{z}{3}=k\)
\(\Rightarrow x=-4k;y=-7k;z=3k\)(1)
Thay (1) vào ta có :
\(A=\dfrac{-2x+y+5z}{2x-3y-6z}=\dfrac{-2.\left(-4k\right)+\left(-7k\right)+5.3k}{2.\left(-4k\right)-3.\left(-7k\right)-6.3k}=\dfrac{8k+-7k+15k}{\left(-8k\right)-\left(-27k\right)-18k}=\dfrac{k\left(8+-7+15\right)}{k\left(-8+27-18\right)}=\dfrac{16}{17}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
x/-4=y/-7=z/3
=-2x+y+5z/-2.(-4)+(-7)+5.3
= 2x-3y-6z/2.(-4)-3.(-7)-6.3
=> -2x+y+5z/16=2x-3y-6z/-5
=> -2x+y+5z/2x-3y-6z
=16/-5
Vậy A = 16/-5
Đặt x/-4=y/-7=z/3=k
=>x=-4k,y=-7k,z=3k(*)
Thay (*) vào A ta có:
A=(-2x+y+5z)/(2x-3y-6z)
=(8k-7k+15k)/(-8k+21k-18k)
=16k/-5k
=16/-5
Vậy A=-16/5
Đặt \(\dfrac{x}{-4}=\dfrac{y}{-7}=\dfrac{z}{3}=k\)
\(\Rightarrow\left\{{}\begin{matrix}x=-4k\\y=-7k\\z=3k\end{matrix}\right.\)
\(\Rightarrow A=\dfrac{-2.\left(-4k\right)+\left(-7k\right)+5.3k}{-4k-3.\left(-7k\right)-6.3k}=\dfrac{16k}{-1k}=-16\)
Đặt x/-4=k => x=-4k
y/-7=k => y=-7k
z/3=k => z=3k
=> A=8k+7k+15k / -8k+21k-18k
A=30k / -5k
=> A=-6
Đặt \(\dfrac{x}{-4}=\dfrac{y}{-7}=\dfrac{z}{3}=k\left(k\ne0\right)\)
=>\(\left\{{}\begin{matrix}x=-4k\\y=-7k\\z=3k\end{matrix}\right.\)
Ta có P =\(\dfrac{-2\cdot\left(-4k\right)+\left(-7k\right)+5\cdot3k}{2\cdot\left(-4k\right)-3\left(-7k\right)-6\left(3k\right)}\)=\(\dfrac{8k+\left(-7k\right)+15k}{-8k+21k-18k}\)=
\(\dfrac{k\cdot\left(8+\left(-7\right)+15\right)}{k.\left(-8+21-18\right)}=\dfrac{-16}{5}\)
Vậy P= \(\dfrac{-16}{5}\)
Theo đề ta có:
\(\dfrac{x}{-4}=\dfrac{y}{-7}=\dfrac{z}{3}\)
Đặt k cho biểu thức trên
=>\(\dfrac{x}{-4}=\dfrac{y}{-7}=\dfrac{z}{3}\) =k
=> \(\left[{}\begin{matrix}\dfrac{x}{-4}=k\\\dfrac{y}{-7}=k\\\dfrac{z}{3}=k\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\left(-4\right).k\\y=\left(-7\right).k\\z=3.k\end{matrix}\right.\)
Thay \(\left[{}\begin{matrix}x=\left(-4\right).k\\y=\left(-7\right).k\\z=3.k\end{matrix}\right.\) vào biểu thức \(P=\dfrac{-2x+y+5z}{2x-3y-6z}\)
Ta được:
\(P=\dfrac{-2.\left(-4.k\right)+\left(-7.k\right)+5\left(3.k\right)}{2\left(-4.k\right)-3\left(-7.k\right)-6\left(3.k\right)}\)
=> \(P=\dfrac{8.k+\left(-7.k\right)+15.k}{-8.k+21.k-18.k}\)
=> \(P=\dfrac{k.\left(8+-7+15\right)}{k.\left(-8+21-18\right)}\)
=> P= \(-\dfrac{16}{5}\)
Vậy:....................
Đặt \(\dfrac{x}{-4}=\dfrac{y}{-7}=\dfrac{z}{3}=k\)
\(\Rightarrow x=-4k;y=-7k;z=3k\) (1)
Thay (1) vào A , ta được
\(A=\dfrac{-2.\left(-4k\right)+\left(-7k\right)+5.3k}{2\left(-4k\right)-3\left(-7k\right)-6.3k}\)
\(\Rightarrow A=\dfrac{8k+\left(-7k\right)+15k}{-8k+21k+\left(-18k\right)}\)
\(\Rightarrow A=\dfrac{k[8+\left(-7\right)+15]}{k[-8+21+\left(-18\right)]}\)
\(\Rightarrow A=\dfrac{16k}{-5k}\)
\(\Rightarrow A=\dfrac{16}{5}\)
Vậy \(A=\dfrac{16}{5}\)