Question 77
Let $a,b,c$ be rational numbers such that $a+bc,b+ac,a+b$ are all nonzero and
$$\frac1{a+bc}+\frac1{b+ac}=\frac1{a+b}.$$
Prove that $\sqrt{(c-3)(c+1)}$ is rational.
$$\frac1{a+bc}+\frac1{b+ac}=\frac1{a+b}.$$
Prove that $\sqrt{(c-3)(c+1)}$ is rational.