Answer:
{42, 56, 69}
Step-by-step explanation:
For repetitive calculations, a spreadsheet or calculator can relieve the tedium. We're asked to evaluate the Pythagorean relation for different number sets. Here, we need to find the set of numbers such that ...
c² ≠ a² +b² . . . . . not a right triangle
This is equivalent to ...
a² +b² -c² ≠ 0
which is the formula we used in the graphing calculator shown in the attachment.
The lengths {42, 56, 69} will not form a right triangle.
_____
Additional comment
The difference of squares form used in f(x) gives a value that is related to the cosine of the largest angle in the triangle:
cos(θ) = f(a, b, c)/(2ab)
The sign of the value of f(x) is positive for acute triangles, negative for obtuse triangles. The largest angle in {42, 56, 69} is about 88.3°.
