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Product of real solutions $x$ of the equation: $x^2+4|x|-4=0$ ?

$4(2\sqrt2-3)$ : Is it the correct answer?

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closed as off-topic by max_zorn, YiFan, Cesareo, Shailesh, darij grinberg Feb 3 at 5:48

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    $\begingroup$ Yes, or at least I get the same answer. $\endgroup$ – Alec B-G Feb 2 at 19:03
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To solve $x^2 + 4|x| - 4 = 0$, consider two cases:

$(1)$ $x \ge 0. $ In this case, the equation is $x^2+4x-4=0$ and the solution is $x=-2+2 \sqrt 2.$ (The other solution to that quadratic equation is negative.)

$(2)$ $x < 0. $ In this case, the equation is $x^2 - 4x - 4=0$ and the solution is $x=2 - 2 \sqrt 2.$ (The other solution to that quadratic equation is positive.)

The product of solutions is therefore $(-2 + 2 \sqrt 2)(2 - 2 \sqrt 2) = -12 + 8 \sqrt 2 ,$ which is the same as the answer you gave.

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