14.3.1 Least square method

Problem: The function \( y=\frac{a}{x}+b x \) is given by the table of the approximate values \begin{tabular}{|c|c|c|c|c|} \hline\( x \) & 0.1 & 0.2 & 0.25 & 0.5 \\ \hline\( y \) & \( 29 \cdot N \) & \( 13 \cdot N \) & \( 10 \cdot N \) & \( 2 \cdot N \) \\ \hline \end{tabular} where \( N \) is the number of the variant. Determine the coefficients \( a, b \) by the least squares method. Calculate the value of the root mean square error. Plot the graphs of the function given in the table and the obtained function. \[ N=2 \]