Tìm x
a) x+y=1/3 b) x.y=3/5
y+z=-1/4 y.z=4/5
z+x=1/5 z.x=3/4
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Tìm các số hữu tỉ x,y,z
x (x+y+z) = -12 ; y (y+x+z) = 18 ; z (z+y+x) = 30
\(\frac{x}{3}=\frac{y}{5};\frac{y}{6}=\frac{z}{7}\)và 3x + y - 2z = 42
x.y = z; y.z = 4x ; z.x = 9y
x.y = \(\frac{3}{5};y.z=\frac{4}{5};z.x=\frac{3}{4}\)
tìm x,y,x biết
a)\(\frac{x}{3}=\frac{y}{4};\frac{y}{3}=\frac{z}{5}\)và 2x-3y+z=6
b)\(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)và x.y+y.z+z.x=64
a,\(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\Leftrightarrow\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}=\frac{2x-3y+z}{18-36+20}=\frac{6}{2}=3\)=3
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Timf x,y,z
x.y=-8/5 , y.z=3/4 , z.x=-3/10
Tìm x,y,z biết :
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{Z}{4}\) và x.y+y.z+z.x=104
tìm các số hữu tỉ x ,y,z thảo mãn
x.y=-2/5 ; y.z=3/4 ; z.x=-3/10
\(\Rightarrow\left(x.y.z\right)^2=\frac{-2}{5}.\frac{3}{4}.\frac{-3}{10}\)
\(\Rightarrow\left(x.y.z\right)^2=\frac{18}{200}=\frac{9}{100}\)
\(\Rightarrow x.y.z=\frac{3}{10}\)
\(\Rightarrow z=\frac{3}{-4}\)
\(\Rightarrow x=\frac{2}{5}\)
\(\Rightarrow y=-1\)
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a) Cho 3 số x,y,z biết x.y.z=1. Tính tổng: \(\frac{5}{x+x.y+1}+\frac{5}{y+y.z+1}+\frac{5}{z+z.x+1}\)
b) Cho 3 số x,y,z biết x.y.z=1992. Chứng minh: \(\frac{1992.x}{x.y+1992.x}\)+\(\frac{y}{y.z+y+1992}\)+\(\frac{z}{x.z+z+1}\)=1
Tìm x ; y ;z :
a. x.y = \(\dfrac{1}{2}\) ; y.z=\(\dfrac{3}{5}\) ; z.x=\(\dfrac{27}{10}\)
b. \(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}\) và 5x-3y-4z=46
b)
\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}=\dfrac{5x-5}{10}=\dfrac{3y+9}{12}=\dfrac{4z-20}{24}\)
\(\Rightarrow\dfrac{\left(5x-3y-4z\right)-\left(5+9-20\right)}{10-12-24}=\dfrac{46+6}{-26}=-2\)
\(\Rightarrow x-1=-4\Rightarrow x=-3\)
\(\Rightarrow y+3=-8\Rightarrow y=-11\)
\(\Rightarrow z-5=-12\Rightarrow-7\)
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tìm x,y, z biết:
a) \(x+y=\frac{1}{2},y+z=\frac{1}{3},z+x=\frac{1}{4}\)
b)\(x.y=-\frac{1}{2},y.z=\frac{1}{2},z.x=-\frac{1}{4}\)
a) Cộng cả 3 đẳng thức trên ta có:
2(x + y + z) = 1/2 +1/3 + 1/4 = 13/12 => x + y + z = 13/24 (*)
z = 13/24 - 1/2 = 1/24
x = 13/24 - 1/3 = 5/24
y = 13/24 - 1/4 = 7/24.
b) Nhân cả 3 đẳng thức ta có: x2y2z2 = 1/16 => xyz = 1/4 hoặc -1/4
Nếu xyz = 1/4 thì: z = -1/2; x = 1/2; y = -1Nếu xyz = -1/4 thì: z = 1/2; x = -1/2; y = 1
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Tìm x ; y ; z :
\(x.y=\frac{3}{5}\) ; \(y.z=\frac{4}{5}\) ; \(z.x=\frac{3}{4}\)
\(\left\{{}\begin{matrix}xy=\dfrac{3}{5}\\yz=\dfrac{4}{5}\\zx=\dfrac{3}{4}\end{matrix}\right.\Rightarrow x^2y^2z^2=\dfrac{3}{5}.\dfrac{4}{5}.\dfrac{3}{4}=\dfrac{9}{25}\)
\(\Rightarrow xyz=\pm\dfrac{3}{5}\)
+) \(xyz=\dfrac{3}{5}\Rightarrow\left\{{}\begin{matrix}z=1\\x=\dfrac{3}{4}\\y=\dfrac{4}{5}\end{matrix}\right.\)
+) \(xyz=\dfrac{-3}{5}\Rightarrow\left\{{}\begin{matrix}z=-1\\x=\dfrac{-3}{4}\\y=\dfrac{-4}{5}\end{matrix}\right.\)
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\(\text{Ta có : }xy=\dfrac{3}{5}\\ yz=\dfrac{4}{5}\\ zx=\dfrac{4}{4}\\ \Rightarrow xy\cdot yz\cdot zx=\dfrac{3}{5}\cdot\dfrac{4}{5}\cdot\dfrac{3}{4}\\ \Rightarrow x^2\cdot y^2\cdot z^2=\dfrac{9}{25}\Rightarrow\left(xyz\right)^2=\dfrac{9}{25}\\ \Rightarrow xyz=\dfrac{-3}{5}\text{hoặc : }\\ xyz=\dfrac{3}{5}\)
\(\text{+) Xét }xyz=-\dfrac{3}{5}\Leftrightarrow\left\{{}\begin{matrix}x\cdot\left(yz\right)=-\dfrac{3}{5}\\y\cdot\left(xz\right)=-\dfrac{3}{5}\\z\cdot\left(xy\right)=-\dfrac{3}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\cdot\dfrac{4}{5}=-\dfrac{3}{5}\\y\cdot\dfrac{3}{4}=-\dfrac{3}{5}\\z\cdot\dfrac{3}{5}=-\dfrac{3}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{3}{4}\\y=-\dfrac{4}{5}\\z=-1\end{matrix}\right.\)
\(\text{+) Xét }xyz=\dfrac{3}{5}\Leftrightarrow\left\{{}\begin{matrix}x\cdot\left(yz\right)=\dfrac{3}{5}\\y\cdot\left(xz\right)=\dfrac{3}{5}\\z\cdot\left(xy\right)=\dfrac{3}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\cdot\dfrac{4}{5}=\dfrac{3}{5}\\y\cdot\dfrac{3}{4}=\dfrac{3}{5}\\z\cdot\dfrac{3}{5}=\dfrac{3}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{4}\\y=\dfrac{4}{5}\\z=1\end{matrix}\right.\)
Vậy \(x;y;z=-\dfrac{3}{4};-\dfrac{4}{5};-1\) hoặc \(x;y;z=\dfrac{3}{4};\dfrac{3}{5};1\)
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\(\left\{{}\begin{matrix}x.y=\dfrac{3}{5}\\y.z=\dfrac{4}{5}\\z.x=\dfrac{3}{4}\end{matrix}\right.\)
\(\Rightarrow x.y.y.z.z.x=\dfrac{3}{5}.\dfrac{4}{5}.\dfrac{3}{4}\)
\(\Rightarrow\left(x.y.z\right)^2=\dfrac{9}{25}\)
\(\Rightarrow xyz=\pm\dfrac{9}{25}\)
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