# Product of real solutions of the equation [closed]

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

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

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

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• Yes, or at least I get the same answer. – Alec B-G Feb 2 at 19:03

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.