# need help with this question!

• Mar 25th 2013, 09:13 PM
mathkid182
need help with this question!
If 2 positive numbers differ by 3 and the sum of the squares of these numbers is 120.Find the numbers.?

Any help would be great!
• Mar 25th 2013, 09:21 PM
Prove It
Re: need help with this question!
Let x and y be the two numbers. Then x - y = 3 and $\displaystyle x^2 + y^2 = 120$. Solve the equations simultaneously.
• Mar 25th 2013, 11:54 PM
mathkid182
Re: need help with this question!
hi thanks for the reply. the part you posted is actually the part im stuck on im sure of the next step to solve the equations?
• Mar 25th 2013, 11:55 PM
Prove It
Re: need help with this question!
Start with x = y + 3 and substitute into the second equation.
• Mar 25th 2013, 11:56 PM
mathkid182
Re: need help with this question!
so i would combine the x2 + y2 = 120 into the x=y+3 somehow?
• Mar 25th 2013, 11:58 PM
Prove It
Re: need help with this question!
Quote:

Originally Posted by Prove It
Let x and y be the two numbers. Then x - y = 3 and $\displaystyle x^2 + y^2 = 120$. Solve the equations simultaneously.

Yes, replace the x in $\displaystyle x^2 + y^2 = 120$ with y + 3. This will give you a quadratic equation to solve.
• Mar 26th 2013, 12:02 AM
mathkid182
Re: need help with this question!
im really sorry i just not to sure. would the next step be:

(y+3)^2 + 3 = 120

then

y^2 + 9+3 = 120?
• Mar 26th 2013, 12:56 AM
Prove It
Re: need help with this question!
Almost, (y + 3)^2 = y^2 + 6y + 9, not y^2 + 9. Fix that mistake, simplify, and solve the quadratic equation.
• Mar 26th 2013, 01:26 AM
mathkid182
Re: need help with this question!
so it will be

y2 + 6y + 9 = 120 (take 120 from both side)

= y2 + 6y -117 = 0

and then what I cant fin number that will simply this?
• Mar 26th 2013, 04:00 AM
HallsofIvy
Re: need help with this question!
Sigh. Your left side is (y+ 3)^2. You forgot the other "y^2". Do you know the "quadratic formula" or how to "complete the square"?
You've also done the arithmetic wrong: 9- 120 is NOT equal to -117.