Question

Express 21² as sum of two consecutive natural number and Explain how?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{x}\mathrm{and}\mathrm{x}+1\mathrm{be}2\mathrm{consecutive}\mathrm{natural}\mathrm{numbers}. \\ \mathrm{Now},\mathrm{x}+\mathrm{x}+1={21}^2 \\ \Rightarrow 2\mathrm{x}+1=441 \\ \Rightarrow 2\mathrm{x}=440 \\ \Rightarrow \mathrm{x}=220 \\ \mathrm{Now},\mathrm{first}\mathrm{number}=220 \\ \mathrm{second}\mathrm{number}=220+1=221 \\ \mathrm{So},\mathrm{consecutive}\mathrm{natural}\mathrm{numbers}\mathrm{are}:220\mathrm{and}221 \end{gathered}$$