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1. The problem statement, all variables and given/known data

Let a, b, and c be lengths of sides of triangle T, where a ≤ b ≤ c.

Prove that if T is a right triangle, then (abc)^{2}=(c^{6}-a^{6}-b^{6})/3

2. Relevant equations

If T is a right triangle, then Pythagorean’s Theorem states:

The sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse. That is a^{2}+b^{2}=c^{2}, where c is the hypotenuse.

3. The attempt at a solution

We assume the given equation and using Pythagorean’s Theorem, we obtain solutions for c^{2}and c^{6}:

We substitute these results into the original equation.

This produces an equation where the left hand side is identical to the right hand side.

Since these terms are equal, it follows that the original equation holds true for a right triangle.

This is what I have. I am curious to if the proof is correct/acceptable.

Thanks for any feedback.

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# Homework Help: My proof involving Pythagorean’s Theorem

Can you offer guidance or do you also need help?

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