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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?

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all I want really is a nudge in the right direction

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More than a nudge but...

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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

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Posted (edited)

Sorry, I misread the question.

Edited by HallsofIvy

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

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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

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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.

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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.

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OMG,i don't know the answer for it.

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