(x+y):(8-z):(y+z):(10+z)=2:5:3:4

\(\Rightarrow\)\(\dfrac{x+y}{2}=\dfrac{8-z}{5}=\dfrac{y+z}{3}=\dfrac{10+z}{4}\)

giải ra x=-4;y=8;z=-2

dài lắm

\(\left(x+y\right):\left(8-z\right):\left(y+z\right):\left(10+z\right)=2:5:3:4\\ < =>\dfrac{x+y}{2}=\dfrac{8-z}{5}=\dfrac{y+z}{3}=\dfrac{10-z}{4}\left(1\right)\)

\(\left(1\right)=>\dfrac{8-z}{5}=\dfrac{10+z}{4}\\ < =>4\left(8-z\right)=5\left(10+z\right)\\ < =>32-4z=50+5z\\ < =>-9z=18\\ < =>z=-2\left(2\right)\)

\(\left(1\right)=>\dfrac{y+z}{3}=\dfrac{8-z}{5}\left(3\right)\)

thay (2) vào (3)

\(=>\dfrac{y-2}{3}=\dfrac{8+2}{5}\\ < =>\dfrac{y-2}{3}=2\\ < =>y=8\left(4\right)\)

\(\left(1\right)=>\dfrac{x+y}{2}=\dfrac{8-z}{5}\left(5\right)\)

thay 4 và 2 vào 5

\(=>\dfrac{x+8}{2}=\dfrac{8+2}{5}\\ < =>\dfrac{x+8}{2}=2\\ < =>x=-4\left(6\right)\)

\(=>\dfrac{xyz}{x+y+z}\\ =\dfrac{\left(-2\right).8.\left(-4\right)}{\left(-4\right)+8+\left(-2\right)}\\ =\dfrac{64}{2}\\ =32\)

vậy ...

bài dễ nhưng dài quá @@

chúc may mắn

a) \(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7};x+y+z=56\)

\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{x+y+z}{2+5+7}=\dfrac{56}{14}=4\)

\(\Rightarrow\left\{{}\begin{matrix}x=4.2=8\\y=4.5=20\\z=4.7=28\end{matrix}\right.\)

b) \(\dfrac{x}{1,1}=\dfrac{y}{1,3}=\dfrac{z}{1,4}\left(1\right);2x-y=5,5\)

\(\left(1\right)\Rightarrow\dfrac{2x-y}{1,1.2-1,3}=\dfrac{5,5}{0,9}\)

\(\Rightarrow\left\{{}\begin{matrix}x=1,1.\dfrac{5,5}{0,9}=\dfrac{6,05}{0,9}\\y=1,3.\dfrac{5,5}{0,9}=\dfrac{7,15}{0,9}\\z=\dfrac{1,4}{1,1}.x=\dfrac{1,4}{1,1}.\dfrac{6,05}{0,9}=\dfrac{8,47}{0,99}\end{matrix}\right.\)

d) \(\dfrac{x}{2}=\dfrac{x}{3}=\dfrac{z}{5};xyz=-30\)

\(\dfrac{x}{2}=\dfrac{x}{3}=\dfrac{z}{5}=\dfrac{xyz}{2.3.5}=\dfrac{-30}{30}=-1\)

\(\Rightarrow\left\{{}\begin{matrix}x=2.\left(-1\right)=-2\\y=3.\left(-1\right)=-3\\z=5.\left(-1\right)=-5\end{matrix}\right.\)

a) �2=�5=�7;�+�+�=562x​=5y​=7z​;x+y+z=56

�2=�5=�7=�+�+�2+5+7=5614=42x​=5y​=7z​=2+5+7x+y+z​=1456​=4

⇒{�=4.2=8�=4.5=20�=4.7=28⇒⎩⎨⎧​x=4.2=8y=4.5=20z=4.7=28​

b) �1,1=�1,3=�1,4(1);2�−�=5,51,1x​=1,3y​=1,4z​(1);2x−y=5,5

(1)⇒2�−�1,1.2−1,3=5,50,9(1)⇒1,1.2−1,32x−y​=0,95,5​
    

⇒⎩⎨⎧​x=1,1.0,95,5​=0,96,05​y=1,3.0,95,5​=0,97,15​z=1,11,4​.x=1,11,4​.0,96,05​=0,998,47​​

d) �2=�3=�5;���=−302x​=3x​=5z​;xyz=−30

�2=�3=�5=���2.3.5=−3030=−12x​=3x​=5z​=2.3.5xyz​=30−30​=−1

⇒{�=2.(−1)=−2�=3.(−1)=−3�=5.(−1)=−5⇒⎩⎨⎧​x=2.(−1)=−2y=3.(−1)=−3z=5.(−1)=−5​
 

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