Question 25
In triangle $ABC$ with side lengths $a,b,c$, it is known that $b+c=6$ and its area satisfies $S=a^2-(b-c)^2$. Find the largest possible value of $S$.
Answer entry: use a reduced fraction a/b, without spaces. The checker recognizes only explicitly listed exact strings, not arbitrary equivalent expressions. An unrecognized equivalent form requires manual checking and must not be treated as wrong or scored zero solely for nonrecognition.
Answer entry: use a reduced fraction a/b, without spaces. The checker recognizes only explicitly listed exact strings, not arbitrary equivalent expressions. An unrecognized equivalent form requires manual checking and must not be treated as wrong or scored zero solely for nonrecognition.