An Ultimate Chinese High-School Maths Problem

Question Solve \[\sqrt[3]{a+\frac{a+1}{3}\cdot \sqrt{\frac{8a-1}{3}}}+\sqrt[3]{a-\frac{a+1}{3}\cdot \sqrt{\frac{8a-1}{3}}}\] Solution: From the question, we regulate \[\begin{align*} \frac{8a-1}{3}&\geq 0\\ a&\geq \frac{1}{8} \end{align*}\] Let \[\xi…

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An Interesting High-School Maths Problem

Question Given \[f\left ( x \right )-\frac{1}{3}f\left ( \frac{x}{3} \right )=x,\] find \(f\left ( x \right )\). Alternative solution: We derive the following equations, \[f\left ( x \right )-\frac{1}{3}f\left ( \frac{x}{3} \right )=x\] \[\frac{1}{3^{1}}f\left…

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