Question

Express 15² as the sum of two consecutive integers.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{x}\mathrm{and}\mathrm{x}+1\mathrm{be}2\mathrm{consecutive}\mathrm{integers}. \\ \mathrm{Now},\mathrm{x}+\mathrm{x}+1={15}^2 \\ \Rightarrow 2\mathrm{x}+1=225 \\ \Rightarrow 2\mathrm{x}=224 \\ \Rightarrow \mathrm{x}=\frac{224}{2}=112 \\ \mathrm{Now},\mathrm{consecutive}\mathrm{integers}\mathrm{are}112\mathrm{and}113. \\ \mathrm{Now},112+113=225={15}^2 \end{gathered}$$