Dumb Dad needs help for daughter?

Question

Two numbers when added equal 10.260. When the two numbers are multiplied together they again equal 10.260. What are the two numbers? She got the answer using a trig calculator but does not know how the calculator got the answer and she needs to show the work. Doing it my way by trial and error is not acceptable. Anyone know how to write out the formulas for this?

Answer 1

This is solved by a "system of equations".

Let a equal the first number and b equal the second one:

Equation 1) → a + b = 10.260

Equation 2) → a * b = 10.260

In equation1, solve for b:

a + b = 10.260

b = -a + 10.260

Now substitute this result into equation 2:

a * b = 10.260

a * (-a + 10.260a) = 10.260

-a^2 + 10.260a - 10.260 = 0 ← (This becomes equation #3)

Since equation 3 does not factor, use the quadratic formula:

a = [-b ± sqrt(b^2 - 4ac)] / 2a

a = 1.1228938122381 and 9.1371061877619

Back to equation 1:

a + b = 10.260

1.1228938122381 + b = 10.26

b = 9.1371061877619

a + b = 10.260

9.1371061877619 + b = 10.26

b = 1.1228938122381

* * * * * * * * * * * * * *

ALWAYS CHECK YOUR WORK

* * * * * * * * * * * * * *

1.1228938122381 + 9.1371061877619 = 10.260 ← Checks!

1.1228938122381 *  9.1371061877619 = 10.260 ← Checks!

For more information on how to do these types of problems:

http://www.purplemath.com/modules/systli...

Good luck with your daughter's studies,

~ Mitch ~