1. ## 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!

2. ## Re: Sequencing problem

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 $\displaystyle m^2+(m-6)^2=90$.

3. ## 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?

4. ## Re: Sequencing problem

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 $\displaystyle m-n=6$ ...?

5. ## Re: Sequencing problem

Shouldn't it be the difference for the first equation $\displaystyle m-n=6$ ...?