spydragon

a^2+b^2=2(c^2)

Recommended Posts

this is not an assignment I was given but it is something I've been thinking about and I don't know how to solve it

I want a list of equations that use two variables that when I plug in any whole number value for the two variables they will give me solutions to the equation (a^2) + (b^2) = 2(c^2)

an example of what I want is the Pythagorean triples.

(a^2) + (b^2) = c^2

a = 2mn

b = (m^2) - (n^2)

c = (m^2) + (n^2)

can someone help me with this problem?

Share this post


Link to post
Share on other sites
Posted (edited)

should have clarified that, even though I am a fan of mathematics I have only learned pre algebra through part of geometry

(and I don't know if what I want exists), thank you anyway

Edited by spydragon

Share this post


Link to post
Share on other sites

Spydragon: do you understand the reasoning behind the equations you gave for a^2 + b^2 = c^2?

Share this post


Link to post
Share on other sites

 

12 hours ago, uncool said:

Spydragon: do you understand the reasoning behind the equations you gave for a^2 + b^2 = c^2?

 uncool, yes but my reasoning goes only as far as a video I watched on how to do it. I used the same method but got an annoying square root of 2 to mess it up

Share this post


Link to post
Share on other sites
On 4/8/2019 at 8:56 AM, uncool said:

Spydragon: do you understand the reasoning behind the equations you gave for a^2 + b^2 = c^2?

@uncool yes but my reasoning goes as far as a video I watched on how to get it. I used the same method but got an annoying square root of 2 to mess it up.

Share this post


Link to post
Share on other sites

What do you think is the reasoning behind those equations? In other words, I'm not talking about whether they work, but why they work - what train of thought led to their discovery. There is some interesting geometric reasoning that immediately gives the answer for a^2 + b^2 = 2c^2.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now