Question

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Answer 1

\[\begin{array}{l}
a)\frac{x}{2} = \frac{y}{5};\;x.y\; = \;10\\
= > x = \frac{2}{5}y\\
x.y\; = \;10\\
= > \frac{2}{5}y.y = 10\\
= > {y^2} = 25\\
= > \left[ \begin{array}{l}
y = - 5\\
y = 5
\end{array} \right.\\
+ )y = - 5 = > x = \frac{2}{5}\left( { - 5} \right) = - 2\\
+ )y = 5 = > x = \frac{2}{5}.5 = 2\\
vay:\left( {x;y} \right) = \left( { - 2; - 5} \right);\left( {2;5} \right)\\
b)\frac{x}{2} = \frac{y}{3}\\
= > x = \frac{{2y}}{3}\\
\frac{y}{4} = \frac{z}{5}\;\\
= > z = \frac{{5y}}{4}\\
x + y - z\; = \;100\;\\
= > \frac{{2y}}{3} + y - \frac{{5y}}{4} = 100\\
= > \frac{5}{{12}}y = 100\\
= > y = 240\\
= > x = 240.\frac{2}{3} = 160\\
z = \frac{5}{4}.240 = 300\\
vay:\left( {x;y;z} \right) = \left( {160;240;300} \right)\\
c)\frac{2}{x} = \frac{3}{y}\;\left( {x;y \ne 0} \right)\\
= > \frac{x}{2} = \frac{y}{3}\\
= > x = \frac{2}{3}y\\
\;xy = 96\\
= > \frac{2}{3}y.y = 96\\
= > {y^2} = 144\\
= > \left[ \begin{array}{l}
y = 12\\
y = - 12
\end{array} \right.\\
+ )y = 12 = > x = \frac{2}{3}.12 = 8\\
+ )y = - 12 = > x = \frac{2}{3}\left( { - 12} \right) = - 8\\
vay:\left( {x;y} \right) = \left( { - 8; - 12} \right);\left( {8;12} \right)
\end{array}\]

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Answer 2

\[\begin{array}{l}
a)\frac{x}{2} = \frac{y}{5};\;x.y\; = \;10\\
= > x = \frac{2}{5}y\\
x.y\; = \;10\\
= > \frac{2}{5}y.y = 10\\
= > {y^2} = 25\\
= > \left[ \begin{array}{l}
y = - 5\\
y = 5
\end{array} \right.\\
+ )y = - 5 = > x = \frac{2}{5}\left( { - 5} \right) = - 2\\
+ )y = 5 = > x = \frac{2}{5}.5 = 2\\
vay:\left( {x;y} \right) = \left( { - 2; - 5} \right);\left( {2;5} \right)\\
b)\frac{x}{2} = \frac{y}{3}\\
= > x = \frac{{2y}}{3}\\
\frac{y}{4} = \frac{z}{5}\;\\
= > z = \frac{{5y}}{4}\\
x + y - z\; = \;100\;\\
= > \frac{{2y}}{3} + y - \frac{{5y}}{4} = 100\\
= > \frac{5}{{12}}y = 100\\
= > y = 240\\
= > x = 240.\frac{2}{3} = 160\\
z = \frac{5}{4}.240 = 300\\
vay:\left( {x;y;z} \right) = \left( {160;240;300} \right)\\
c)\frac{2}{x} = \frac{3}{y}\;\left( {x;y \ne 0} \right)\\
= > \frac{x}{2} = \frac{y}{3}\\
= > x = \frac{2}{3}y\\
\;xy = 96\\
= > \frac{2}{3}y.y = 96\\
= > {y^2} = 144\\
= > \left[ \begin{array}{l}
y = 12\\
y = - 12
\end{array} \right.\\
+ )y = 12 = > x = \frac{2}{3}.12 = 8\\
+ )y = - 12 = > x = \frac{2}{3}\left( { - 12} \right) = - 8\\
vay:\left( {x;y} \right) = \left( { - 8; - 12} \right);\left( {8;12} \right)
\end{array}\]

Answer 3

$a, \frac{x}{2} = \frac{y}{5} \Leftrightarrow x = \frac{2}{5} y M à x . y = 10 n ê n \frac{2}{5} y . y = 10 \Leftrightarrow y^{2} = 25 \Leftrightarrow y = 5 h o ặ c y = - 5 y = 5 t h ì x = \frac{2}{5} . 5 = 2 y = - 5 t h ì x = \frac{2}{5} . (- 5) = - 2$

Vậy x=2 thì y=5; x=-2 thì y=-5

$b, \frac{x}{2} = \frac{y}{3} \Leftrightarrow x = \frac{2}{3} y \frac{y}{4} = \frac{z}{5} \Leftrightarrow z = \frac{5}{4} y M à x + y - z = 100 n ê n \frac{2}{3} y + y - \frac{5}{4} y = 100 \Leftrightarrow \frac{5}{12} y = 100 \Leftrightarrow y = 100 : \frac{5}{12} = 240 x = \frac{2}{3} . 240 = 160 z = \frac{5}{4} . 240 = 300$

Vậy x=160,y=240 ,z=300

$c, \frac{2}{x} = \frac{3}{y} \Rightarrow x = \frac{2}{3} y (x; y \neq 0) M à x . y = 96 n ê n \frac{2}{3} y . y = 96 \Leftrightarrow y^{2} = 144 \Leftrightarrow y = \pm 12 x = \frac{2}{3} y = \pm 8$

Vậy x=8 thì y=12; x=-8 thì y=-12

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Answer 4

$a, \frac{x}{2} = \frac{y}{5} \Leftrightarrow x = \frac{2}{5} y M à x . y = 10 n ê n \frac{2}{5} y . y = 10 \Leftrightarrow y^{2} = 25 \Leftrightarrow y = 5 h o ặ c y = - 5 y = 5 t h ì x = \frac{2}{5} . 5 = 2 y = - 5 t h ì x = \frac{2}{5} . (- 5) = - 2$

Vậy x=2 thì y=5; x=-2 thì y=-5

$b, \frac{x}{2} = \frac{y}{3} \Leftrightarrow x = \frac{2}{3} y \frac{y}{4} = \frac{z}{5} \Leftrightarrow z = \frac{5}{4} y M à x + y - z = 100 n ê n \frac{2}{3} y + y - \frac{5}{4} y = 100 \Leftrightarrow \frac{5}{12} y = 100 \Leftrightarrow y = 100 : \frac{5}{12} = 240 x = \frac{2}{3} . 240 = 160 z = \frac{5}{4} . 240 = 300$

Vậy x=160,y=240 ,z=300

$c, \frac{2}{x} = \frac{3}{y} \Rightarrow x = \frac{2}{3} y (x; y \neq 0) M à x . y = 96 n ê n \frac{2}{3} y . y = 96 \Leftrightarrow y^{2} = 144 \Leftrightarrow y = \pm 12 x = \frac{2}{3} y = \pm 8$

Vậy x=8 thì y=12; x=-8 thì y=-12

Answer 5

a)x2=y5;x.y=10=>x=25yx.y=10=>25y.y=10=>y2=25=>[y=−5y=5+)y=−5=>x=25(−5)=−2+)y=5=>x=25.5=2vay:(x;y)=(−2;−5);(2;5)

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