দুটি অসম রাশির গাণিতিক গড় এবং ভেদাংক যথাক্রমে $12$ এবং $36$ হলে রাশি দুটির মান কত?

ধরি, সংখ্যা দুটি $\mathrm{x}_{1}, \mathrm{x}_{2} \quad \therefore$ গড় $=\frac{x_{1}+x_{2}}{2}$ ভেদাঙ্ক $=\frac{\left(x_{1}-12\right)^{2}+\left(x_{2}-12\right)^{2}}{2}$ এখন, $\frac{\mathrm{x}_{1}+\mathrm{x}_{2}}{2}=12 \therefore \mathrm{x}_{1}+\mathrm{x}_{2}=24 \therefore \mathrm{x}_{1}=24-\mathrm{x}_{2} \ldots \ldots \ldots \ldots \text { (i) }$ $\therefore \frac{\left(x_{1}-12\right)^{2}+\left(x_{2}-12\right)^{2}}{2}=36 \Rightarrow\left(x_{1}-12\right)^{2}+\left(x_{2}-12\right)^{2}=72$ $\begin{array}{l}\Rightarrow\left(24-x_{2}-12\right)^{2}+\left(x_{2}-12\right)^{2}=72 \Rightarrow 2 \times\left(x_{2}-12\right)^{2}=72 \\\therefore\left(x_{2}-12\right)^{2}=36 \therefore x_{2}=12+6=18 \therefore x_{1}=(24-18) \text { or, } 6\end{array}$