# 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
3. Add 1 to 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
$\displaystyle (n - 1)(n + 1) = n^2 - 1$

3. Add 1 to your number
$\displaystyle n^2$

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
$\displaystyle (n - 1)(n + 1) = n^2 - 1$

3. Add 1 to your number
$\displaystyle n^2$

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.