Question

The roots of \(2x-\frac{2}{x}= 3\) are 

• A. \(1,\frac{1}{2}\)
• B. 2,1
• C. \(2,\frac{1}{2}\)
• D. None

Answer 1

The Correct Option is C

We are given the equation: \[ 2x - \frac{2}{x} = 3 \] Multiply both sides by \( x \) to eliminate the denominator: \[ 2x^2 - 2 = 3x \] Rearrange the terms to form a quadratic equation: \[ 2x^2 - 3x - 2 = 0 \] Now solve for \( x \) using the quadratic formula: \[ x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(2)(-2)}}{2(2)} \] \[ x = \frac{3 \pm \sqrt{9 + 16}}{4} = \frac{3 \pm \sqrt{25}}{4} \] \[ x = \frac{3 \pm 5}{4} \] So, the roots are: \[ x = \frac{3 + 5}{4} = \frac{8}{4} = 2 \quad \text{and} \quad x = \frac{3 - 5}{4} = \frac{-2}{4} = -\frac{1}{2} \]

The correct option is (C): \(2,\frac{1}{2}\)