Question 15
(ISR 2) IMO5. The nonnegative real numbers $x_1,x_2,x_3,x_4,x_5,a$ satisfy the following relations:
$$\sum_{i=1}^5ix_i=a,\qquad\sum_{i=1}^5i^3x_i=a^2,\qquad\sum_{i=1}^5i^5x_i=a^3.$$
What are the possible values of $a$?
$$\sum_{i=1}^5ix_i=a,\qquad\sum_{i=1}^5i^3x_i=a^2,\qquad\sum_{i=1}^5i^5x_i=a^3.$$
What are the possible values of $a$?