6 Given that $a, b, c$ are all real numbers greater than 0, let proposition $P$ be: the segments of lengths $a, b, c$ can form the three sides of a triangle, and proposition $Q: a^{2}+b^{2}+c^{2}<2(ab+bc+$ (a), then $P$ is $Q$'s ( ).
(A) sufficient but not necessary condition
(B) necessary but not sufficient condition
(C) sufficient and necessary condition
(D) neither sufficient nor necessary condition
6 A Hint: On one hand, if $P$ holds, then $b+c>a$, so $a(b+c)>a^{2}$, which means $a b+a c>a^{2}$.
Similarly, $b a+b c>b^{2}, c a+c b>c^{2}$. Therefore,
$$
a^{2}+b^{2}+c^{2}<2(a b+b c+c a),
$$

which means $Q$ holds.
On the other hand, if $Q$ holds, take $b=c=1, a=2$, at this time the segments of lengths $a, b, c$ cannot form the three sides of a triangle, so $P$ does not hold.
In summary, $P$ is a sufficient but not necessary condition for $Q$.