Áp dụng t/c dtsbn:

\(\dfrac{x}{12}=\dfrac{y}{13}=\dfrac{z}{15}=\dfrac{x+y+z}{12+13+15}=\dfrac{160}{40}=4\)

\(\Rightarrow\left\{{}\begin{matrix}x=4.12=48\\y=4.13=52\\z=4.15=60\end{matrix}\right.\)

\(\frac{x+11}{13}=\frac{y+12}{14}=\frac{z+13}{15}.\)

\(\Rightarrow\frac{x+11}{13}=\frac{y+12}{14}=\frac{z+13}{15}=\frac{x+11+y+12+z+13}{13+14+15}=\frac{\left(x+y+z\right)+\left(11+12+13\right)}{42}\)

\(=\frac{6+36}{42}=\frac{42}{42}=1\)  ( Áp dụng tính chất dãy tỉ số bằng nhau )

\(\Rightarrow\hept{\begin{cases}\frac{x+11}{13}=1\\\frac{y+12}{14}=1\\\frac{z+13}{15}=1\end{cases}}\Rightarrow\hept{\begin{cases}x+11=13\\y+12=14\\z+13=15\end{cases}}\Rightarrow\hept{\begin{cases}x=2\\y=2\\z=2\end{cases}}\)

Vậy \(x=y=z=2\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có :

\(\frac{x+11}{13}=\frac{y+12}{14}=\frac{z+13}{15}=\frac{x+11+y+12+z+13}{13+14+15}\)

\(=\frac{\left(x+y+z\right)+\left(11+12+13\right)}{13+14+15}=\frac{16+36}{42}=\frac{42}{42}=1\)

\(\Rightarrow\frac{x+11}{13}=1\Rightarrow x+11=13\Rightarrow x=13-11=2\)

\(\Rightarrow\frac{y+12}{14}=1\Rightarrow y+12=14\Rightarrow y=14-12=2\)

\(\Rightarrow\frac{z+13}{15}=1\Rightarrow z+13=15\Rightarrow z=15-13=2\)

Vậy \(x=y=z=2\)

C1:

\(\text{Ta có: }\frac{x+11}{13}=\frac{y+12}{14}=\frac{z+13}{15};x+y+z=6\left(1\right)\)

\(\text{Áp dụng tính dãy tỉ số bằng nhau: }\)

\(\Rightarrow\frac{x+11}{13}=\frac{y+12}{14}=\frac{z+13}{15}=\frac{\left(x+11\right)+\left(y+12\right)+\left(z+13\right)}{13+14+15}=\frac{x+11+y+12+z+13}{42}=\frac{\left(x+y+z\right)+\left(11+12+13\right)}{42}\left(2\right)\)

\(\text{Thay (1) và (2), ta được: }\)

\(\frac{6+36}{42}=\frac{42}{42}=1\)

\(\Rightarrow\left\{{}\begin{matrix}\frac{x+11}{13}=1\\\frac{y+12}{14}=1\\\frac{z+13}{15}=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x+11=13\\y+12=14\\z+13=15\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\\y=2\\z=2\end{matrix}\right.\)

\(\text{Vậy }x=2;y=2;z=2\)

C2:

\(x+y+z=6\left(1\right)\)

\(\text{Ta có: }\frac{x+11}{13}=\frac{y+12}{14}\Rightarrow x+11=\frac{y+12}{14}.13\Rightarrow x=\frac{13.\left(y+12\right)}{14}-11\)

\(\frac{y+12}{14}=\frac{z+13}{15}\Rightarrow z+13=\frac{y+12}{14}.15\Rightarrow z=\frac{15.\left(y+12\right)}{14}-13\)

\(\text{Thay }x=\frac{13.\left(y+12\right)}{14}-11;z=\frac{15.\left(y+12\right)}{14}-13\text{ vào }\left(1\right)\)

\(\Rightarrow\frac{13.\left(y+12\right)}{14}-11+y+\frac{15.\left(y+12\right)}{14}-13=6\)

\(\Leftrightarrow\frac{13.\left(y+12\right)}{14}+y+\frac{15.\left(y+12\right)}{14}-\left(11+13\right)=6\)

\(\Leftrightarrow\frac{13.\left(y+12\right)}{14}+\frac{14y}{14}+\frac{15.\left(y+12\right)}{14}-24=6\)

\(\Leftrightarrow\frac{13.\left(y+12\right)+14y+15.\left(y+12\right)}{14}=6+24\)

\(\Leftrightarrow\frac{\left(y+12\right).\left(13+15\right)+14y}{14}=30\)

\(\Leftrightarrow\left(y+12\right).28+14y=30.14\)

\(\Leftrightarrow14.\left[\left(y+12\right).2+y\right]=420\)

\(\Leftrightarrow2y+12.2+y=420:14\)

\(\Leftrightarrow3y+24=30\)

\(\Leftrightarrow3y=30-24\)

\(\Leftrightarrow3y=6\)

\(\Leftrightarrow y=6:3\)

\(\Leftrightarrow y=2\)

\(\text{Khi đó: }x=\frac{13.\left(2+12\right)}{14}-11\left(\text{Do y=2}\right)\)

\(\Leftrightarrow x=\frac{13.14}{14}-11\)

\(\Leftrightarrow x=13-11\)

\(\Leftrightarrow x=2\)

\(\text{Khi đó: }z=\frac{15.\left(2+12\right)}{14}-13\left(\text{Do y=2}\right)\)

\(\Leftrightarrow z=\frac{15.14}{14}-13\)

\(\Leftrightarrow z=15-13\)

\(\Leftrightarrow z=2\)

\(\text{Vậy }x=2;y=2;z=2\)

A

Chọn A

Theo đề bài :

\(\frac{x+11}{13}=\frac{y+12}{14}=\frac{z+13}{13}\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có :

\(\frac{x+11}{13}=\frac{y+12}{14}=\frac{z+13}{13}=\frac{x+y+z+36}{40}=\frac{21}{20}\)

=> \(\frac{x+11}{13}=\frac{21}{20}\)

=> \(\frac{y+12}{14}=\frac{21}{20}\)

=> \(\frac{z+13}{13}=\frac{21}{20}\)

Rồi đến đây bạn tự làm nốt đi ha !!!

7) 5x=4y ⇒\(\dfrac{x}{4}=\dfrac{y}{5}\)

Nhân cả hai vế với \(\dfrac{x}{4}\), ta có: \(\left(\dfrac{x}{4}\right)^2=\dfrac{x}{4}.\dfrac{y}{5}=\dfrac{xy}{20}=\dfrac{20}{20}=1\)

\(\left(\dfrac{x}{4}\right)^2=1\Rightarrow\left[{}\begin{matrix}\dfrac{x}{4}=1\\\dfrac{x}{4}=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

⇒ \(\left[{}\begin{matrix}y=5\\y=-5\end{matrix}\right.\)

4) áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{0,5}=\dfrac{y}{0,3}=\dfrac{z}{0,2}=\dfrac{z-y+x}{0,2-0,3+0,5}=\dfrac{1}{\dfrac{2}{5}}=\dfrac{5}{2}\)

\(\dfrac{x}{0,5}=\dfrac{5}{2}\Rightarrow x=\dfrac{5}{4}\)

\(\dfrac{y}{0,3}=\dfrac{5}{2}\Rightarrow y=\dfrac{3}{4}\)

\(\dfrac{z}{0,2}=\dfrac{5}{2}\Rightarrow z=\dfrac{1}{2}\)

6) áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x+11}{13}=\dfrac{y+12}{14}=\dfrac{z+13}{15}=\dfrac{x+11+y+12+z+13}{13+14+15}=\dfrac{42}{42}=1\)

\(\dfrac{x+11}{13}=1\Rightarrow x=2\)

\(\dfrac{y+12}{13}=1\Rightarrow y=1\)

\(\dfrac{z+13}{15}=1\Rightarrow z=2\)

7) \(5x=4y\Rightarrow\dfrac{x}{4}=\dfrac{y}{5}=k\)

\(\Rightarrow x=4k,y=5k\)

\(x.y=20\\ \Rightarrow4k.5k=20\\ \Rightarrow20k^2=20\\ \Rightarrow k^2=1\\ \Rightarrow\left[{}\begin{matrix}k=-1\\k=1\end{matrix}\right.\)

\(x=4k\Rightarrow\left[{}\begin{matrix}x=-4\\x=4\end{matrix}\right.\)

\(y=5k\Rightarrow\left[{}\begin{matrix}y=-5\\y=5\end{matrix}\right.\)

Vậy \(\left(x,y\right)=\left\{\left(-4;-5\right);\left(4;5\right)\right\}\)

\(\frac{13}{38}>\frac{13}{39}=3=\frac{12}{36}>\frac{12}{37}=\frac{-12}{-37}\)

Vậy: \(\frac{13}{38}>\frac{-12}{-37}\)

\(\frac{13}{38}\) > \(\frac{13}{39}\) = \(\frac13\) = \(\frac{-12}{-36}\) > \(\frac{-12}{-37}\)

\(\frac{13}{38}>\frac{13}{39}=\frac{1}{3}=\frac{12}{36}>\frac{12}{37}\)

Ta có:1-13/38=25/38

1-12/37=25/37

Do 25/37>25/38 =>13/38>12/37

Vậy 13/38>12/37