The product of 2 numbers is 504. The difference between the 2 numbers is 10. What is the bigger number?

MaiaMitchell Aug 5, 2015

#1**+10 **

Hi Maia,

a+b=10

so

b=10-a

ab=504

a(10-a)=504

-a^2+10a-504=0

a^2-10a+504=0

$${{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{504}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{a}} = {\mathtt{5}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{479}}}}{\mathtt{\,\times\,}}{i}\\

{\mathtt{a}} = {\sqrt{{\mathtt{479}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}\\

\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{a}} = {\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{21.886\: \!068\: \!628\: \!239\: \!289\: \!2}}{i}\\

{\mathtt{a}} = {\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{21.886\: \!068\: \!628\: \!239\: \!289\: \!2}}{i}\\

\end{array} \right\}$$

There are no real solutions to this .

Melody Aug 5, 2015

#1**+10 **

Best Answer

Hi Maia,

a+b=10

so

b=10-a

ab=504

a(10-a)=504

-a^2+10a-504=0

a^2-10a+504=0

$${{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{504}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{a}} = {\mathtt{5}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{479}}}}{\mathtt{\,\times\,}}{i}\\

{\mathtt{a}} = {\sqrt{{\mathtt{479}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}\\

\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{a}} = {\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{21.886\: \!068\: \!628\: \!239\: \!289\: \!2}}{i}\\

{\mathtt{a}} = {\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{21.886\: \!068\: \!628\: \!239\: \!289\: \!2}}{i}\\

\end{array} \right\}$$

There are no real solutions to this .

Melody Aug 5, 2015

#2**0 **

i think you made a slight error here, Melody....we have

A - B = 10 → B =A - 10 and AB = 504 ...so we have

A(A - 10) = 504

A^2 - 10A - 504 = 0 factor

(A + 18) (A - 28) = 0

Then, either A = -18 and B = -28 or A = 28 and A = 18

CPhill Aug 5, 2015