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\(A=\left|3-x\right|+8\ge8\)
\(minA=8\Leftrightarrow x=3\)
\(B=\left|x+2\right|-4\ge-4\)
\(minB=-4\Leftrightarrow x=-2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left|x-201\right|+\left|x-204\right|=\left|x-201\right|+\left|204-x\right|\ge\left|x-201+204-x\right|=\left|3\right|=3\)
\(minA=3\Leftrightarrow\left(x-201\right)\left(204-x\right)\ge0\Leftrightarrow204\ge x\ge201\)
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\(\frac{3}{4}x=\frac{1}{2}y=\frac{3}{2}z\) và x - y = -10
Ta có : \(\frac{3}{4}x=\frac{1}{2}y=\frac{3}{2}z\)=> \(\frac{3x}{4}=\frac{y}{2}=\frac{3z}{2}\)=> \(\frac{x}{\frac{4}{3}}=\frac{y}{2}=\frac{z}{\frac{2}{3}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{\frac{4}{3}}=\frac{y}{2}=\frac{z}{\frac{2}{3}}=\frac{x-y}{\frac{4}{3}-2}=\frac{-10}{\left(-\frac{2}{3}\right)}=15\)
=> \(\hept{\begin{cases}\frac{x}{\frac{4}{3}}=15\\\frac{y}{2}=15\\\frac{z}{\frac{2}{3}}=15\end{cases}}\Rightarrow\hept{\begin{cases}x=20\\y=30\\z=10\end{cases}}\)
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Ap dung tinh chat day ti so bang nhau ta co :
x-1/2=y-2/3=z-3/4=(x-1)-2(y-2)+3(z-3)/2-2.3+3.4=x-1+2y+4+3z-9/2-6+12=(x-2y+3z)+(-1+4-9)=-10-6/8=-2
Suy ra : x-1/2=-2=>x-1=-4=>x=-3
y-2/3=-2=>y-2=-6=>y=-4
z-3/4=-2=>z-3=-8=>z=-5
nho lik e nhe
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{\left(x-1\right)-2\left(y-2\right)+3\left(z-3\right)}{2-2.3+3.4}=\frac{\left(x-2y+3z\right)+\left(-1+4-9\right)}{2-6+12}=\frac{-10-6}{8}=-2\)
x-1 = -2.2 =-4 => x = -3
+y-2 = -2 .3 =-6 => y =-4
z -3 =-2.4 =-8 => z =-5
![](https://rs.olm.vn/images/avt/0.png?1311)
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đặt \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=k\)(k\(\in\)Z)
=>x-1=2k=>x=2k+1
y-2=3k=>y=3k+2
z-3=4k=>z=4k+3
thay x=2k+1;y=3k+2;z=4k+3 vào x-2y+3z=-10 ta được :
2k+1-2(3k+2)+3(4k+3)=-10
2k+1-6k-4+12k+9=-10
8k+6=-10
8k=-10-6
8k=-16
k=-2
=>x=2k+1=2.(-2)+1=-4+1=-3
=>y=3k+2=3.(-2)+2=-6+2=-4
=>z=4k+3=4.(-2)+3=-8+3=-5
vậy x=-3;y=-4;z=-5
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
ap dung tinh chat day ti so bang nhau ta co :
x-1/2=y-2/3=z-3/4=(x-1)-2.(y-2)+3.(z-3)/2-2.3+3.4
=x-1-2y+4+3z-9/2-6+12 = (x-2y+3z)+(-1+4-9)/8
= 14-6/8
=1
Suy ra :
x-1/2=1=>x-1=2=>x=3
y-2/3=1=>y-2=3=>y=5
z-3/4=1=>z-3=4=>z=7
nho lik e nhe thanks
\(A=|x+3|+y^2-2y+10\)
\(A=|x+3|+\left(y-1\right)^2+9\)
Ta có: \(|x+3|\ge0\forall x\)
\(\left(y-1\right)^2\ge0\forall y\)
\(\Rightarrow|x+3|+\left(y-1\right)^2\ge0\forall x,y\)
\(\Rightarrow|x+3|+\left(y-1\right)^2\ge0+9\forall x,y\)
Hay \(A\ge9\forall x,y\)
Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}x+3=0\\y-1=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-3\\y=1\end{cases}}}\)
Vậy Min A =9\(\Leftrightarrow\hept{\begin{cases}x=-3\\y=1\end{cases}}\)