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

+5
591
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The product of 2 numbers is 504. The difference between the 2 numbers is 10. What is the bigger number?

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 .

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
#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   Aug 5, 2015
#3
+5

Yes it is one for me and one for you tonight Chris.

I saw 'sum' instead of 'difference'.  Sorry Maia.

Aug 5, 2015
#4
+5

Aren't you going to give yourself 3 points Chris ?  :)

Aug 5, 2015
#5
+5

You cannot give yourself 3 points and I can't give you 3 points either.

You are right, the forum is playing up!  Maybe it just doesn't like you tonight?   :))

Aug 5, 2015