Question 72
Given numbers $r,q,n$ such that
$$\frac1{r+qn}+\frac1{q+rn}=\frac1{r+q},$$
prove that $\sqrt{\frac{n-3}{n+1}}$ is rational.
$$\frac1{r+qn}+\frac1{q+rn}=\frac1{r+q},$$
prove that $\sqrt{\frac{n-3}{n+1}}$ is rational.
MathNet 2014 Question 72
Math Olympiad Vault · MathNet 2014