Question

The difference between the square of two consecutive integers is 47 . Find the numbers .

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{consecutive}\mathrm{integers}\mathrm{be}\mathrm{x}\mathrm{and}\mathrm{x}+1. \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}, \\ {\left(\mathrm{x}+1\right)}^2-{\mathrm{x}}^2=47 \\ \Rightarrow {\mathrm{x}}^2+1+2\mathrm{x}-{\mathrm{x}}^2=47 \\ \Rightarrow 2\mathrm{x}+1=47 \\ \Rightarrow 2\mathrm{x}=47-1 \\ \Rightarrow 2\mathrm{x}=46 \\ \Rightarrow \mathrm{x}=\frac{46}{2}=23 \\ \mathrm{So},\mathrm{consecutive}\mathrm{integers}\mathrm{are}23\mathrm{and}24. \end{gathered}$$