Multiple choice

Solve x + y = x2 - y2 = 23 and find the value of y.

  1. 11

  2. 12

  3. 24

  4. 36
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A Correct answer
Explanation

x + y = 23. x^2 - y^2 = (x+y)(x-y) = 23. Since x+y = 23, then 23(x-y) = 23, so x-y = 1. We have x+y=23 and x-y=1. Adding them: 2x = 24 => x=12. Subtracting: 2y = 22 => y=11.

AI explanation

Using the difference of squares formula on x^2 - y^2 = 23 gives (x - y)(x + y) = 23. Substituting x + y = 23 into this yields (x - y)(23) = 23, meaning x - y = 1. Solving the system x + y = 23 and x - y = 1 gives 2x = 24, so x = 12, and substituting x back gives y = 11.

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