Question 83
There exists a unique triple $(a, b, c)$ of positive real numbers that satisfies the equations
$$2(a^{2} + 1) = 3(b^{2} + 1) = 4(c^{2} + 1) \quad \mathrm{and} \quad ab + bc + ca = 1.$$
Compute $a + b + c$.
$$2(a^{2} + 1) = 3(b^{2} + 1) = 4(c^{2} + 1) \quad \mathrm{and} \quad ab + bc + ca = 1.$$
Compute $a + b + c$.