Multiple choice

Solve the following quadratic equation using quadratic formula: $x+\dfrac{1}{x}=2\dfrac{1}{2}$

  1. $\left \{ \dfrac{1}{2}, 2 \right \}$
  2. $\left \{ \dfrac{1}{2}, -2 \right \}$
  3. $\left \{ \dfrac{-1}{2}, 2 \right \}$

  4. None of these
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A Correct answer
Explanation

x + 1/x = 5/2. Multiply by 2x: 2x^2 + 2 = 5x. 2x^2 - 5x + 2 = 0. (2x - 1)(x - 2) = 0. Roots are 1/2 and 2.

AI explanation

Rewrite the mixed number in the given equation to get x + 1/x = 5/2. Multiplying the entire equation by 2x yields the standard quadratic equation 2x^2 - 5x + 2 = 0. Using the quadratic formula, we find the discriminant b^2 - 4ac equals (-5)^2 - 4(2)(2), which is 9. The roots are calculated as (5 + 3) / 4 and (5 - 3) / 4, resulting in the solution set {2, 1/2}.

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