Question 91
Let $a$, $b$, $c$ be real numbers which satisfy the conditions: $a \lt b \lt c$, $a + b + c = 6$, $ab + bc + ca = 9$. Prove that the inequality
$$
a^2 + b^2 + c^2 - a - 4b - 7c + 15 \lt 0
$$
$$
a^2 + b^2 + c^2 - a - 4b - 7c + 15 \lt 0
$$