# Thread: Algebra math tricks/puzzle - Equivalences in Algebra

1. ## Algebra math tricks/puzzle - Equivalences in Algebra

I have an equivalent algebra math problem and I still don't know how you solve it.
It starts like:
1. Take a number
2. Multiply the two numbers on either side of your number
4. Take the square root of this answer
5. What do you notice?
6. Prove this is true for any number

Now I know that the prove means it has to have some type of algebra in it. But what I get stuck on is 5. What do you notice
Can somebody help please because it has really been annoying me
Thank you

2. ## Re: Algebra math tricks/puzzle - Equivalences in Algebra

1. Take a number
$\displaystyle n$

2. Multiply the two numbers on either side of your number
$\displaystyle (n - 1)(n + 1) = n^2 - 1$

$\displaystyle n^2$

4. Take the square root of this answer
$\displaystyle n$

-Dan

3. ## Re: Algebra math tricks/puzzle - Equivalences in Algebra

Originally Posted by topsquark
1. Take a number
$\displaystyle n$

2. Multiply the two numbers on either side of your number
$\displaystyle (n - 1)(n + 1) = n^2 - 1$

$\displaystyle n^2$

4. Take the square root of this answer
$\displaystyle n$
Example where the number chosen doesn't equal the final number:

The number I take is -9.

(-9 - 1)(-9 + 1) = (-10)(-8) = 80

80 + 1 = 81

$\displaystyle 81 = 9^2$

$\displaystyle \sqrt{9^2} = |9| = 9$ **

** $\displaystyle \sqrt{x^2} = |x|$

4. ## Re: Algebra math tricks/puzzle - Equivalences in Algebra

Thank you so much this has really helped me!!!

5. ## Re: Algebra math tricks/puzzle - Equivalences in Algebra

Originally Posted by greg1313
Example where the number chosen doesn't equal the final number
1. Take a number: $\displaystyle \pi$
2. Multiply the two numbers on either side of your number: "the two numbers on either side of your number" is not well defined so the multiplication cannot be done.

1 3 5 7 ...
1 4 9 16...

7. ## Re: Algebra math tricks/puzzle - Equivalences in Algebra

Originally Posted by Archie
1. Take a number: $\displaystyle \pi$
2. Multiply the two numbers on either side of your number: "the two numbers on either side of your number" is not well defined so the multiplication cannot be done.
True but I would have interpreted "the two numbers on either side of your number" as indicated that the "numbers" referred to here are integers.