Question 31
a) Prove that there exist irrational numbers $a$, $b$, and $c$ so that the numbers $a+bc$, $b+ac$ and $c+ab$ are rational.
b) Prove that, if the real numbers $a$, $b$, and $c$ are such that $a + b + c = 1$ and the numbers $a+bc$, $b+ac$, and $c+ab$ are non-zero rationals, then the numbers $a$, $b$, $c$ are rational.
b) Prove that, if the real numbers $a$, $b$, and $c$ are such that $a + b + c = 1$ and the numbers $a+bc$, $b+ac$, and $c+ab$ are non-zero rationals, then the numbers $a$, $b$, $c$ are rational.