Isn't that odd?

Algebra Level 3

How many real solutions $x$ are there to $|17-|x^{2}-2|| = 15$ ?

The answer is 5.

2 solutions

Jake Lai
Dec 21, 2014

First, we graph the parabola $y = x^{2}$ , shift it down 2 units, and reflect the part with negative $y$ across the $x$ -axis. After shifting the parabola down 17 units, we reflect the part with negative $y$ across the across the $x$ -axis again. What we have drawn is $y = |17-|x^{2}-2||$ .

Finally, we draw the line $y = 15$ . The two curves intersect at 5 points, and so there are 5 real solutions in total.

Keith Fife
Dec 23, 2014

That's a pretty tedious solution, but it's purely algebraic so kudos on that. It would be much clearer if you could separate the proof into cases and then subcases.

It might be better to write in LaTeX; there's a formatting guide in-site and lots of resources on the interwebs.

Jake Lai - 6 years, 5 months ago

Isn't that odd?

The answer is 5.

2 solutions

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