Question

I am thinking of a number. When I subtract 25 from my, than square the answer. I get same result when I square my number then sutract 25 from the answers. What is my number?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{x}\mathrm{be}\mathrm{the}\mathrm{number}. \\ \mathrm{According}\mathrm{to}\mathrm{question}, \\ {\left(\mathrm{x}-25\right)}^2={\mathrm{x}}^2-25 \\ \Rightarrow {\mathrm{x}}^2-50\mathrm{x}+{\left(25\right)}^2={\mathrm{x}}^2-25\left(\mathrm{Using}\mathrm{identity},{\left(\mathrm{a}-\mathrm{b}\right)}^2={\mathrm{a}}^2-2\mathrm{ab}+{\mathrm{b}}^2\right) \\ \Rightarrow -50\mathrm{x}+625=-25 \\ \Rightarrow -50\mathrm{x}=-25-625 \\ \Rightarrow -50\mathrm{x}=-650 \\ \Rightarrow \mathrm{x}=13 \\ \mathrm{Hence},\mathrm{the}\mathrm{number}\mathrm{is}625. \end{gathered}$$