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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

Hi;

A square is drawn with one of its sides on the line y = 10. The endpoints of this side lie on the parabola y = x^2 + 5x + 4. What is the area of that square?

We will use geogebra!

1)Enter in the input bar f(x)=x^2=5*x+4. The parabola will be drawn.

2)Enter in the input bar f(y)=10. The horizontal line will be drawn.

3)Find the points of intersection of the parabola and the line y = 10 by using the intersection tool. They will be labelled B and C.

4)Use B and C and the regular polygon tool to make a square with B and C as the bottom vertices of the square.

5)Check in the algebra pane what poly1 is.

We are done! Check that your construction looks like mine.

Now get this. This was posted on one of the most prestigious forums on earth. Loaded with super mathematicians and olympiad hopefuls. Only two people answered this and one of them got it wrong!

Now I know dozens of them could do this problem. But to them it is nothing but pure drudgery. You have to solve a quadratic and then use the distance formula, not a lot of fun. By using an interactive geometry program it is fun and you get the right answer.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Hmmm ... the roots of y = x^2 + 5x + 4 **- 10** = x^2 + 5x - 6 are -6 and 1, so the side length is 7 and area is 49

(I did use my Quadratic Equation Solver to find the roots)

Or did I misunderstand the question?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

Hi MIF;

That solution is good.

In my desire to change the problem, it became easier to solve it algebraically than to use the program! It is a rare talent to keep shooting your own foot off. I seem to be more consistent than most at it.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

I did have the advantage of your illustration.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

Hi;

You maybe did not need it. When you saw the plus, minus roots the side of the square can easily be determined.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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