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Philippine Mathematical Olympiad

Algebra Difficulty 5.0 AIME Prove it Philippines

Problem:
How many real number solutions does the equation $\frac{1}{3} x^{4} + 5|x| = 7$ have?

Solution

Solution:
The solutions correspond to intersection points of $y = 7 - \frac{1}{3} x^{4}$ and $y = 5|x|$ . Clearly, there are only two intersection points.

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