সহায়িকা

\begin{aligned}
&\text{দেওয়া আছে, } a^{2} + \frac{1}{a^{2}} = 51 \\
&\text{বা, } \left( a - \frac{1}{a} \right)^{2} + 2 \cdot a \cdot \frac{1}{a} = 51 \\
&\text{বা, } \left( a - \frac{1}{a} \right)^{2} + 2 = 51 \\
&\text{বা, } \left( a - \frac{1}{a} \right)^{2} = 51 - 2 \\
&\text{বা, } \left( a - \frac{1}{a} \right)^{2} = 49 \\
&\therefore a - \frac{1}{a} = \pm 7
\end{aligned}

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