Multiple choice

The sum of all real roots of the equation $ x^{2}+15=8|x| $ is

  1. $0$
  2. $6$
  3. $10$
  4. $16$
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A Correct answer
Explanation

The equation is x^2 - 8|x| + 15 = 0. Let u = |x|, then u^2 - 8u + 15 = 0, which factors to (u-3)(u-5) = 0. So |x| = 3 or |x| = 5. The roots are 3, -3, 5, -5. The sum is 3 + (-3) + 5 + (-5) = 0.

AI explanation

Factoring the absolute value equation gives the solutions |x| = 3 and |x| = 5. This yields four real roots: x = 3, x = -3, x = 5, and x = -5. The sum of these real roots is 3 + (-3) + 5 + (-5) = 0.

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