# I double dare you to expand.

**Algebra**Level 4

Let the real positive solution of

\[x^{2} + \left(\frac{x}{x+1}\right)^{2} = 1\]

be \( \alpha \). Find the value of \( \lfloor 10000 \alpha \rfloor \).

Let the real positive solution of

\[x^{2} + \left(\frac{x}{x+1}\right)^{2} = 1\]

be \( \alpha \). Find the value of \( \lfloor 10000 \alpha \rfloor \).

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