# Sequencing problem

• Jul 26th 2013, 01:58 PM
curt26
Sequencing problem
The difference of two positive numbers is 6 and the sum of their squares is 90. Find the numbers.

I know the numbers are 3 and 9, but I just don't know how to go about showing the work.

Thanks!
• Jul 26th 2013, 02:30 PM
Plato
Re: Sequencing problem
Quote:

Originally Posted by curt26
The difference of two positive numbers is 6 and the sum of their squares is 90. Find the numbers.
I know the numbers are 3 and 9, but I just don't know how to go about showing the work.

Given \$\displaystyle m-n=6~\&~m^2+n^2=90\$ so \$\displaystyle m^2+(m-6)^2=90\$.
• Jul 26th 2013, 02:32 PM
Re: Sequencing problem
You just need to translate this into a system of equations.

\$\displaystyle x-y=6\$

\$\displaystyle x^2+y^2=90\$

So you can start off:

\$\displaystyle x=y+6\$

\$\displaystyle (y+6)^2+y^2=90\$

\$\displaystyle (y^2+12y+36) +y^2=90\$

\$\displaystyle 2y^2+12y-54=0\$

Do you see how to take it from here?
• Jul 26th 2013, 02:33 PM
Re: Sequencing problem
Quote:

Originally Posted by Plato
Given \$\displaystyle m+n=6~\&~m^2+n^2=90\$ so \$\displaystyle m^2+(6-m)^2=90\$.

Shouldn't it be the difference for the first equation \$\displaystyle m-n=6\$ ...?
• Jul 26th 2013, 03:16 PM
Plato
Re: Sequencing problem
Quote: