Question
The numbers a, b, c are different from 0, and the numbers ab, ac, bc are rational.
a. Show that `a^2+b^2+c^2` is a rational number.
b. Show that if `a^3+b^3+c^3` is a rational number, then `a+b+c` is a rational number.
Difficulty level (1 very easy - 10 very hard): 3
Sources:
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