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# Algebraic Manipulation

Gauss, Ramanujan, and a pantheon of other mathematicians have given us algebraic manipulation tools way beyond what's taught in school. Learn what they knew.

If \[x^{\frac{1}{2}}+x^{-\frac{1}{2}}=10,\] what is the value of \(x+x^{-1}\)?

If \( a = b + 4 \), what is the value of

\[ 3 a - 3 b + 3 ? \]

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