To determine if the numbers 8, 6, and 9 form a Pythagorean triple, we need to identify the largest number, which will be considered as \( c \) (the hypotenuse), and the other two as \( a \) and \( b \). In this case, 9 is the largest number, so we will consider:
- \( a = 6 \)
- \( b = 8 \)
- \( c = 9 \)
A Pythagorean triple satisfies the equation:
\[ a^2 + b^2 = c^2 \]
Now, let's calculate \( a^2 + b^2 \) and \( c^2 \):
- Calculate \( a^2 + b^2 \):
\[ 6^2 + 8^2 = 36 + 64 = 100 \]
- Calculate \( c^2 \):
\[ 9^2 = 81 \]
Now, we compare \( a^2 + b^2 \) and \( c^2 \):
- \( a^2 + b^2 = 100 \)
- \( c^2 = 81 \)
Since \( 100 \neq 81 \), the numbers do not satisfy the equation \( a^2 + b^2 = c^2 \).
Thus, the correct answer is:
No, because the given numbers do not satisfy the equation \( a^2 + b^2 = c^2 \).