To determine if the set of numbers \( (5, 7, \sqrt{74}) \) forms a Pythagorean triple, we need to check if the following equation holds:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the largest number. From the given set, we identify \( a = 5 \), \( b = 7 \), and \( c = \sqrt{74} \).
Now, we compute:
- \( a^2 = 5^2 = 25 \)
- \( b^2 = 7^2 = 49 \)
- \( c^2 = (\sqrt{74})^2 = 74 \)
Now we add \( a^2 \) and \( b^2 \):
\[ a^2 + b^2 = 25 + 49 = 74 \]
And compare it with \( c^2 \):
\[ c^2 = 74 \]
Since \( a^2 + b^2 = c^2 \) holds true, we conclude that:
Yes, it is a Pythagorean triple.
1 answer