Multiple choice

Find the roots of the following quadratic equations by using the quadratic formula $\displaystyle \frac{x}{x - 1} + \frac{x - 1}{x} = 4, x \neq 0, 1$

  1. $\displaystyle \frac{2 \pm \sqrt 3}{4}$
  2. $\displaystyle \frac{-1 \pm \sqrt 3}{2}$
  3. $\displaystyle \frac{1 \pm \sqrt 3}{1}$
  4. $\displaystyle \frac{-2 \pm \sqrt 3}{4}$
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C Correct answer
AI explanation

Multiply the entire equation by the common denominator x times the quantity x minus 1 to get x squared plus the quantity x minus 1 squared equals 4x times the quantity x minus 1. Expanding and simplifying this results in the quadratic equation 2x squared minus 6x plus 1 equals 0. Using the quadratic formula with a equal to 2, b equal to negative 6 and c equal to 1, the roots are 6 plus or minus the square root of 36 minus 8, all divided by 4, which simplifies to 1 plus or minus the square root of 3.

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