1

Part of 2009 German National Olympiad

Problems(1)

Cube roots in an equation

Source: Germany 2009 - Problem 1

Find all non-negative real numbers

a

such that the equation

\sqrt[3]{1+x}+\sqrt[3]{1-x}=a

has at least one real solution

x

0 \leq x \leq 1

a

x

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