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\(a.\dfrac{6}{5}=\dfrac{18}{x}\Rightarrow x=\dfrac{18\cdot5}{6}=15\\ \text{Vậy}\text{ }x=15.\)
\(b.\dfrac{3}{4}=\dfrac{-21}{x}\Rightarrow x=\dfrac{-21\cdot4}{3}=28\\ \text{ }\text{ }\text{ }\text{ }\text{Vậy }x=28.\)
\(c.\dfrac{x}{4}=\dfrac{21}{28}\Rightarrow x=\dfrac{21\cdot4}{28}=3\\ \text{Vậy }x=3.\)
\(d.\dfrac{-8}{2x}=\dfrac{3}{-9}\Rightarrow x=\dfrac{-8\cdot\left(-9\right)}{3}:2=12\\ \text{Vậy }x=12.\)
\(e.\dfrac{-4}{11}=\dfrac{x}{22}=\dfrac{40}{z}\\ \Rightarrow x=\dfrac{-4\cdot22}{11}=-8\\ \Rightarrow z=\dfrac{22\cdot40}{-8}=-110\\ \text{Vậy }x=-8;z=-110.\)
\(f.\dfrac{-3}{4}=\dfrac{x}{20}=\dfrac{21}{y}\\ \Rightarrow x=\dfrac{-3\cdot20}{4}=-15\\ \Rightarrow y=\dfrac{21\cdot20}{-15}=-28\\ \text{Vậy }x=-15;y=-28.\)
\(g.\dfrac{-4}{8}=\dfrac{x}{-10}=\dfrac{-7}{y}=\dfrac{z}{-24}\\ \Rightarrow x=\dfrac{-4\cdot\left(-10\right)}{8}=5\\ \Rightarrow y=\dfrac{-7\cdot\left(-10\right)}{5}=14\\ \Rightarrow z=\dfrac{-7\cdot\left(-24\right)}{14}=12\\ \text{Vậy }x=5;y=14;z=12.\)
\(h.\dfrac{x}{4}=\dfrac{9}{x}\\ \Rightarrow x\cdot x=9\cdot4\\ \Rightarrow x\cdot x=36\\ \Rightarrow x\cdot x=6\cdot6\\ \text{Vậy }\text{cả hai }x=6.\)
a,A=|x-7|+12
Vì \(\left|x-7\right|\ge0\forall x\)nên \(\left|x-7\right|+12\ge12\forall x\)
Ta thấy A=12 khi |x-7| = 0 => x-7 = 0 => x = 7
Vậy GTNN của A là 12 khi x = 7
b,B=|x+12|+|y-1|+4
Vì \(\left|x+12\right|\ge0\forall x\)
\(\left|y-1\right|\ge0\forall y\)
nên \(\left|x+12\right|+\left|y-1\right|\ge0\forall x,y\)
\(\Rightarrow\left|x+12\right|+\left|y-1\right|+4\ge4\forall x,y\)
Ta thấy B = 4 khi \(\hept{\begin{cases}\left|x+12\right|=0\\\left|y-1\right|=0\end{cases}}\Rightarrow\hept{\begin{cases}x+12=0\\y-1=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-12\\y=1\end{cases}}\)
Vậy GTNN của B là 4 khi x = -12 và y = 1
Bài 9:
Ta có: \(\dfrac{12}{-6}=\dfrac{x}{5}=\dfrac{-y}{3}=\dfrac{z}{-17}=\dfrac{-t}{-9}\)
\(\Leftrightarrow\dfrac{x}{5}=\dfrac{-y}{3}=\dfrac{-z}{17}=\dfrac{t}{9}=-2\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{5}=-2\\\dfrac{-y}{3}=-2\\\dfrac{-z}{17}=-2\\\dfrac{t}{9}=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-10\\-y=-6\\-z=-34\\t=-18\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-10\\y=6\\z=34\\t=-18\end{matrix}\right.\)
Vậy: (x,y,z,t)=(-10;6;34;-18)
Bài 11:
Ta có: \(\dfrac{-7}{6}=\dfrac{x}{18}=\dfrac{-98}{y}=\dfrac{-14}{z}=\dfrac{t}{102}=\dfrac{u}{-78}\)
\(\Leftrightarrow\dfrac{x}{18}=\dfrac{-98}{y}=\dfrac{-14}{z}=\dfrac{t}{102}=\dfrac{u}{-78}=\dfrac{-7}{6}\)
Ta có: \(\dfrac{x}{18}=\dfrac{-7}{6}\)
\(\Leftrightarrow x=\dfrac{18\cdot\left(-7\right)}{6}=-21\)
Ta có: \(\dfrac{-98}{y}=\dfrac{-7}{6}\)
\(\Leftrightarrow y=\dfrac{-98\cdot6}{-7}=84\)
Ta có: \(\dfrac{-14}{z}=\dfrac{-7}{6}\)
\(\Leftrightarrow z=\dfrac{-14\cdot6}{-7}=12\)
Ta có: \(\dfrac{u}{-78}=\dfrac{-7}{6}\)
\(\Leftrightarrow u=\dfrac{-78\cdot\left(-7\right)}{6}=\dfrac{78\cdot7}{6}=91\)
Ta có: \(\dfrac{t}{102}=\dfrac{-7}{6}\)
\(\Leftrightarrow t=\dfrac{-7\cdot102}{6}=-7\cdot17=-119\)
Vậy: (x,y,z,t,u)=(-21;84;12;-119;91)
* x/5= -12/50 => x/5= -6/25 => 25x= -6 x 5 => 25x= -30 => x= -6/5
* 2/y=11/ -66 => 2/y= 1/ -6 => y= -6 x 2 => y= -12
* -3/6=x/ -2= -18/y= -z/24
Ta có: -3/6=x/-2 => 6x= -3 x ( -2) => 6x= 6 => x=1
Có: -3/6= -18/y => -3y = -18 x 6 => -3y= -108 => y=36
Lại có: -3/6= -z/24 => -6z= -3 x 24 => -6z= -72 => z= 12
1. x/5 = -12/50
=> x . 50 = 5 . ( -12 )
=> x . 50 = -60
=> x = -60 : 50
=> x = -6/5
2/y = 11/-66
=> 2/y = -11/66 = -1/6
=> 2 . 6 = -y
=> 12 = -y
=> y = -12
-3/6 = x/-2 = -18/y = -z/24
Ta có : -3/6 = x/-2
=> -3 . ( -2 ) = 6x
=> 6 = 6x
=> x = 1
1/-2 = -18/y
=> y = ( -2 ) . ( -18 ) = 36
-18/36 = -z/24
=> -18 . 24 = 36 . ( -z )
=> -432 = 36 . ( -z )
=> -z = -432 : 36 = -12
=> z = 12
Vậy x = 1 ; y = 36 ; z = 12
a,x/5=-12/20
=>4x/20=-12/20
=>4x=-12
=>x=-3
b,2/y=11/-66
=>2/y=1/-6
=>2/y=2/-12
=>y=-12
c,-3/6=x/-2=-18/y=z/24
=>-1/2=x/-2=-18/y=z/24
=>1/-2=x/-2 và -18/36=-18/y và -12/24=z/24
=>x=1,y=36,z=24
d, cái này do quá nhiều đáp án nên mình ko ghi chi tiết ra được
e,3/x+2=5/2x+1
=>3(2x+1)=5(x+2)
=>6x+3=5x+10
=>6x-5x=10-3
=>x=7
a, x=-3
b,x=-12
c,x=1,y=36,z=-12
d,y=4,x=-2 hoặc y=-4,x=2 hoặc y=2,x=-4 hoặc y=-2,x=4
e,x=7