Solve: \(\frac{x}{3} + \frac{3}{x} = 4\frac{1}{4}\)

Q.Solve: \(\frac{x}{3} + \frac{3}{x} = 4\frac{1}{4}\)

\(\frac{x}{3} + \frac{3}{x} = 4\frac{1}{4}\) Or, \(\frac{x^2 + 9}{3x} = \frac{17}{4}\) Or, \(4(x^2 + 9) = 51x\) Or, \(4x^2 + 36 = 51x\) Or, \(4x^2 - 51x + 36 = 0\) Or, \(4x^2 - (48 + 3)x + 36 = 0\) Or, \(4x^2 - 48x - 3x + 36 = 0\) Or, \(4x(x - 12) - 3(x - 12) = 0\) Or, \((x - 12)(4x - 3) = 0\) Therefore, either \((x - 12) = 0\), i.e., \(x = 12\) Or, \((4x - 3) = 0\), i.e., \(x = \frac{3}{4}\) Hence, the required solutions are \(x = 12\) or \(x = \frac{3}{4}\) (Answer)