Question Number 213001 by efronzo1 last updated on 28/Oct/24
$$\:\:\:\:\:\:\underline{\underbrace{\lessdot}\cancel{} } \mathrm{14}^{\mathrm{3}} +\mathrm{15}^{\mathrm{3}} +\mathrm{16}^{\mathrm{3}} +…+\mathrm{24}^{\mathrm{3}} +\mathrm{25}^{\mathrm{3}} \\ $$
Commented by Ghisom last updated on 28/Oct/24
$$\mathrm{12} \\ $$
Answered by mehdee7396 last updated on 28/Oct/24
$$\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +…+\mathrm{25}^{\mathrm{3}} =\left(\frac{\mathrm{25}×\mathrm{26}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$$\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +…+\mathrm{13}^{\mathrm{3}} =\left(\frac{\mathrm{13}×\mathrm{14}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$${s}=\left(\mathrm{25}×\mathrm{13}\right)^{\mathrm{2}} −\left(\mathrm{7}×\mathrm{13}\right)^{\mathrm{2}} =\mathrm{13}^{\mathrm{2}} ×\mathrm{24}^{\mathrm{2}} \\ $$$$\Rightarrow{p}=\mathrm{13}×\mathrm{24} \\ $$$$\Rightarrow{p}−\mathrm{300}=\mathrm{12}\: \\ $$$$ \\ $$