Question

For a = 3, b = 4, and c = 5, show that the following are false...

(a^n) + (b^n) = (c^n) for n = 3, 4, 5, 6 and 7

2. For a = 3, b = 4, and c = 5, the following is true...

(a^n) + (b^n) = (c^n) for n = 2.

Answer 1

see below

Explanation:

1. If we subtract c^n from both sides of the equation and substitute the given values for a, b, c, we find the problem is equivalent to showing ...

3^n +4^n -5^n ≠ 0

The attached table (and graph) show this is true (the original equation is FALSE) for values of n other than 2.

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2. As for problem 1, the question is equivalent to showing ...

3^n +4^n -5^n = 0

for n = 2. Again, the attached table (and graph) show this is TRUE.