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Fed [463]
3 years ago
8

Lee is thinking of two Numbers,the product is 18. the quotient is 2

Mathematics
2 answers:
zzz [600]3 years ago
7 0
\begin{cases} x*y=18 \\ \frac{x}{y}=2  \end{cases}\\\\\begin{cases} 2y*y=18 \\ x=2y  \end{cases}\\\\ \begin{cases} 2y^2=18\ \ /:2 \\ x=2y  \end{cases}\\\\\begin{cases}  y^2=9  \\ x=2y \end{cases}\\\\ y^2-9=0\\\\(y-3)(y+3)=0\\y-3=0\ \ \vee \ \ y+3=0\\y=3 \ \ \vee \ \ y=-3

\begin{cases} y=3 \\ x=2y \end{cases}\ \ \vee \ \ \ \ \begin{cases} y=-3 \\ x=2y \end{cases}\\\\ \begin{cases} y=3 \\ x=2*3 \end{cases}\ \ \vee \ \ \ \ \begin{cases} y=-3 \\ x=2*(-3) \end{cases}\\\\ \begin{cases} y=3 \\ x=6 \end{cases}\ \ \vee \ \ \ \ \begin{cases} y=-3 \\ x=-6\end{cases}\\\\


defon3 years ago
6 0
X, y - the numbers

The product is 18.
xy=18

The quotient is 2.
\frac{x}{y}=2 \ \ \ |\times y \\
x=2y

Substitute 2y for x in the 1st equation:
2y \times y=18 \\
2y^2=18 \ \ \ |\div 2 \\
y^2=9 \\
y=\pm \sqrt{9} \\
y=3 \ \lor \ y=-3 \\ \\
x=2y \\
x=2 \times 3 \ \lor \ x=2 \times (-3) \\
x=6 \ \lor \ x=-6 \\ \\
(x,y)=(6,3) \hbox{ or } (x,y)=(-6,-3)

The numbers are 6 and 3 or -6 and -3.
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