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What multiplies to 33 but adds up to 8?

 Mar 30, 2015

Best Answer 

 #2
avatar+128570 
+5

Nothing......at least in a real number sense......

To see this  let   x be the first number and 8- x the second number...so we have

x (8 - x) = 33      simplify

-x^2 + 8x = 33

-x^2 + 8x - 33 = 0    multiply through by -1

x^2 - 8x + 33 = 0     using the onsite calculator, we have

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{33}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{4}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{17}}}}{\mathtt{\,\times\,}}{i}\\
{\mathtt{x}} = {\sqrt{{\mathtt{17}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{4.123\: \!105\: \!625\: \!617\: \!660\: \!5}}{i}\\
{\mathtt{x}} = {\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4.123\: \!105\: \!625\: \!617\: \!660\: \!5}}{i}\\
\end{array} \right\}$$

Notice that we have solutions.....just not "real" ones.....

 

   

 Mar 30, 2015
 #1
avatar+75 
0

It might be 1 bec. I don't think they have any other numbers in comin.

 Mar 30, 2015
 #2
avatar+128570 
+5
Best Answer

Nothing......at least in a real number sense......

To see this  let   x be the first number and 8- x the second number...so we have

x (8 - x) = 33      simplify

-x^2 + 8x = 33

-x^2 + 8x - 33 = 0    multiply through by -1

x^2 - 8x + 33 = 0     using the onsite calculator, we have

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{33}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{4}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{17}}}}{\mathtt{\,\times\,}}{i}\\
{\mathtt{x}} = {\sqrt{{\mathtt{17}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{4.123\: \!105\: \!625\: \!617\: \!660\: \!5}}{i}\\
{\mathtt{x}} = {\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4.123\: \!105\: \!625\: \!617\: \!660\: \!5}}{i}\\
\end{array} \right\}$$

Notice that we have solutions.....just not "real" ones.....

 

   

CPhill Mar 30, 2015

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