Multiple choice

Find a quadratic equation formed by using the equations x - 2y = 2 and xy = 2.

  1. x2 - 2x - 4 = 0

  2. x2 - 4x - 2 = 0

  3. x2 + 2x - 4 = 0

  4. x2 - 2x + 4 = 0
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A Correct answer
Explanation

Given x - 2y = 2, then y = (x - 2)/2. Substitute into xy = 2: x((x - 2)/2) = 2. This simplifies to x(x - 2) = 4, or x^2 - 2x - 4 = 0.

AI explanation

From the first equation x - 2y = 2, we isolate y to get y = (x - 2) / 2. Substituting this into the second equation xy = 2 results in x multiplied by ((x - 2) / 2), which equals 2. Multiplying the entire equation by 2 and expanding gives x2 - 2x = 4. Rearranging all terms to one side yields the quadratic equation x2 - 2x - 4 = 0.

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