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Given that $$2a+3b=84$$, the largest possible value of $$a\times b$$ is~\uline{~~~~~~~~~~}~. 
Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Forming a Maximum/Minimum Multi-Digit Numbers with Fixed Sums
Given that an unchanged sum, the smaller the difference the larger the product. $84=42+42$$$\Rightarrow (2a) \times (3b)=6ab\leqslant {{42}^{2}}\Rightarrow ab\leqslant 294$$. Thus, the largest possible value of $ab$ is $294$. 