To determine if the tuple (5, 7, √74) is a Pythagorean triple, we need to check if the sum of the squares of the two smaller numbers equals the square of the largest number.
First, identify the sides:
- a = 5
- b = 7
- c = √74 (assuming it's the hypotenuse)
Now, we check if \( a^2 + b^2 = c^2 \):
-
Calculate \( a^2 + b^2 \): \( 5^2 + 7^2 = 25 + 49 = 74 \)
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Calculate \( c^2 \): \( (\sqrt{74})^2 = 74 \)
Now, compare the two results:
- \( a^2 + b^2 = 74 \)
- \( c^2 = 74 \)
Since \( a^2 + b^2 = c^2 \) holds true, (5, 7, √74) is indeed a Pythagorean triple.
Therefore, the answer is 1 for yes.