Quadratic Equation

Date: 04/08/97 at 18:40:09
From: Aaron Hubert
Subject: Solving a system of two equations

I have a word problem that I haven't even started because I don't 
understand it. 

"The sum of two numbers is 15 and their product is 54. Find the 
numbers using a quadratic equation."

Any help would be deeply appreciated.

Date: 04/13/97 at 12:20:51
From: Doctor Steven
Subject: Re: Solving a system of two equations

You have those two equations to solve for. Say the first number is x, 
and the second number is y. Then:

   x + y = 15
   x * y = 54.

Using the first equation:

       y = 15 - x.

Plug this into the second equation to get

       x*(15 - x) = 54.

Simplify the equation:

        15x - x^2 = 54.

Simplify more:

   x^2 - 15x + 54 = 0.

Solve for x using the quadratic equation.  Then y = 15 - x.

Hope this helps.

-Doctor Steven,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/