This course teaches how to install and configure Windows Server 2012 R2. It is the first step on your path to becoming a Microsoft Certified Solutions Expert (MCSE).

Ok. this is an "Extreme Challenge" question, according to my son. I have to admit I am not sure on this one. I have solved it, but not correctly apparently lol

Here we go.

Two real numbers such that one number plus 12.5 equals 1/2 the other number. I Take this to mean: x/2=y+12.5 or y/2 = x+12.5

Additionally, the sum of the squares of those numbers have a difference of 200. I take this as:

X squared - Y squared = 200

or

Y squared-X squared = 200

Solve for X and Y.

The only other statement is that it not need to be in decimal form. An exact fraction is preferred.

My brain hurts.

Here we go.

Two real numbers such that one number plus 12.5 equals 1/2 the other number. I Take this to mean: x/2=y+12.5 or y/2 = x+12.5

Additionally, the sum of the squares of those numbers have a difference of 200. I take this as:

X squared - Y squared = 200

or

Y squared-X squared = 200

Solve for X and Y.

The only other statement is that it not need to be in decimal form. An exact fraction is preferred.

My brain hurts.

Experts Exchange Solution brought to you by

Enjoy your complimentary solution view.

Get every solution instantly with premium.
Start your 7-day free trial.

I wear a lot of hats...

"The solutions and answers provided on Experts Exchange have been extremely helpful to me over the last few years. I wear a lot of hats - Developer, Database Administrator, Help Desk, etc., so I know a lot of things but not a lot about one thing. Experts Exchange gives me answers from people who do know a lot about one thing, in a easy to use platform." -Todd S.

But I see no "sum of the squares" in "Y squared-X squared = 200"

On the other hand, since "the sum of the squares of those numbers" is a single number, I don't understand with what it would have a difference of 200

But if you meant the sum of the squares of those numbers

My wording was off previously... my apologies.

What the heck does that mean????

y=2x+25

Y squared-X squared = 200

(2x+25)^2 - x^2 = 200

3x^2 + 100x + 425 = 0

or,

X squared-Y squared = 200

x^2 - (2x+25)^2 = 200

-3x^2 - 100x - 825 = 0

x = (100 ± 10)/-6

y/2 = x+12.5

(2x+25)^2 - x^2 = -200

So x = 2y + 25

Then

(2y+25)^2 - y^2 = 200

(4y^2 +100y + 625) - y^2 = 200

3y^2 + 100y + 425 = 0

y = -100 +/- Sqrt[100^2 - (4)(3)(425)] / (2)(3) (Quadratic Formula)

y = -100 +/- Sqrt[4900] / 6

y = (-100 +/- 70) / 6

y = -170/6 or y = -30/6 = -5

Then x = 2y + 25 (can be left to the reader).

Experts Exchange Solution brought to you by

Your issues matter to us.

Facing a tech roadblock? Get the help and guidance you need from experienced professionals who care. Ask your question anytime, anywhere, with no hassle.

Start your 7-day free trial1. Write the linear equation (no squares in it) so that x = some stuff with y in it.

2. Write the quadratic equation (the one with squares in it) substituting the "some stuff with y in it" for x.

3. Multiply out any complex terms, add and subtract like terms, until you have something of the form

ay^2 + by + c = 0

4. Apply the Quadratic Formula to solve for y (two solutions).

5. Apply the linear equation in 1 above, to solve for x.

Quadratic Formula: http://en.wikipedia.org/wiki/Quadratic_formula

When he sees the graphs, maybe he'll come up with some repetitious, computative approach on getting the answer without actually solving the problem like others have done above. He could then give a presentation and his interest in math may be sparked (or not).

For your interest, here are two solutions:

x + 12.5 = y/2; x^2 - y^2 = 200

http://www.wolframalpha.com/input/?i=x+%2B+12.5+%3D+y%2F2%3B+x%5E2+-+y%5E2+%3D+200

x + 12.5 = y/2; x^2 - y^2 = -200

http://www.wolframalpha.com/input/?i=x+%2B+12.5+%3D+y%2F2%3B+x%5E2+-+y%5E2+%3D+-200

Math / Science

From novice to tech pro — start learning today.

Question has a verified solution.

Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.

Have a better answer? Share it in a comment.

Experts Exchange Solution brought to you by

Enjoy your complimentary solution view.

Get every solution instantly with premium.
Start your 7-day free trial.

>> the sum of the squares of those numbers have a difference of 200

Did you see this problem in official print or verbally or in notes?

"sum of the squares of those numbers" is a common math expression meaning:

(X squared + Y squared)

whereas your expression: X squared - Y squared might be read as difference between two squares.

If you can get a look at the text of the official problem, it would be interesting to see if it matches your statement.