1. Find another Pythagorean triple.

Question

UpStudy AI · Accepted Answer

A Pythagorean triple consists of three positive integers $$a$$, $$b$$, and $$c$$ such that $$a^2 + b^2 = c^2$$.

To find another Pythagorean triple, we can use the formula:

$$
a = m^2 - n^2, \quad b = 2mn, \quad c = m^2 + n^2
$$

where $$m$$ and $$n$$ are positive integers with $$m > n$$.

Let's choose $$m = 3$$ and $$n = 2$$:

1. Calculate $$a$$:
   $$
   a = 3^2 - 2^2 = 9 - 4 = 5
   $$

2. Calculate $$b$$:
   $$
   b = 2 \cdot 3 \cdot 2 = 12
   $$

3. Calculate $$c$$:
   $$
   c = 3^2 + 2^2 = 9 + 4 = 13
   $$

Thus, the Pythagorean triple is $$(5, 12, 13)$$.

To verify:
$$
5^2 + 12^2 = 25 + 144 = 169 = 13^2
$$

Therefore, $$(5, 12, 13)$$ is indeed a Pythagorean triple.
Another Pythagorean triple is (5, 12, 13).

Solución de tutoría real