Question 158
Consider the following system of 10 equations in 10 real variables $v_1, \dots, v_{10}$:
$$
v_i = 1 + \frac{6 v_i^2}{v_1^2 + v_2^2 + \dots + v_{10}^2} \quad (i = 1, \dots, 10).
$$
Find all 10-tuples $(v_1, v_2, \dots, v_{10})$ that are solutions of this system.
$$
v_i = 1 + \frac{6 v_i^2}{v_1^2 + v_2^2 + \dots + v_{10}^2} \quad (i = 1, \dots, 10).
$$
Find all 10-tuples $(v_1, v_2, \dots, v_{10})$ that are solutions of this system.