Maths Olympiad Prep

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Algebra Difficulty 5.0 AIME Prove it Philippines

Problem:
How many real number solutions does the equation 13x4+5x=7\frac{1}{3} x^{4} + 5|x| = 7 have?

Solution

Solution:
The solutions correspond to intersection points of y=713x4y = 7 - \frac{1}{3} x^{4} and y=5xy = 5|x|. Clearly, there are only two intersection points.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.