Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Right Triangle Prove

Suppose that m and n are positive integers with m > n. c = m^2 + n^2, If a = m^2 - b^2, b = 2mn and c = m^2 + n^2, show that a, b, and c are the lengths of the sides of a right triangle. (This formula can be used to find the sides of a right triangle that are integers, such as 3, 4, 5; 5, 12, 13; and so on. Such triplets of integers are called Pythagorean triples.)

Let me see.

I obviously have to use a^2 + b^2 = c^2.

Here is my set up:

(m^2 - n^2)^2 + (2mn)^2 = (m^2 + n^2)^2

Correct set up?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Right Triangle Prove

You have to prove that the left hand side = the right hand side.

So writing that they are equal is a bit ahead of yourself.

Rather start with LHS =  (m^2 - n^2)^2 + (2mn)^2 , expand and simplfy.

Finally factorise, hopefuly ending up with the RHS.

Bob

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mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Right Triangle Prove

You have to prove that the left hand side = the right hand side.

So writing that they are equal is a bit ahead of yourself.

Rather start with LHS =  (m^2 - n^2)^2 + (2mn)^2 , expand and simplfy.

Finally factorise, hopefuly ending up with the RHS.

Bob

Ok. I get it. Do one side at a time until LHS = RHS.