Question 104
Suppose that the real numbers $x, y, z$ satisfy equalities
$$
15(x + y + z) = 12(xy + yz + zx) = 10(x^2 + y^2 + z^2)
$$
and that at least one of them is different from zero.
a) Prove that $x + y + z = 4$.
b) Find the smallest interval $(a, b)$, which contains all three numbers from any triplet $(x, y, z)$ satisfying the given conditions.
$$
15(x + y + z) = 12(xy + yz + zx) = 10(x^2 + y^2 + z^2)
$$
and that at least one of them is different from zero.
a) Prove that $x + y + z = 4$.
b) Find the smallest interval $(a, b)$, which contains all three numbers from any triplet $(x, y, z)$ satisfying the given conditions.