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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.

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Express \(y\) in terms of \(x\).

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Pranay Singh**

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\[\Large\sqrt[3]{3\sqrt[3]{3\sqrt[3]{3\cdots}}}=\sqrt{n} \quad, \quad n = \ ? \]

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Victor Loh**

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\(x=\sqrt { 2+\sqrt { 2+\sqrt { 2+\sqrt { 2\ldots } } } } \)

What is the value of \(x\)?

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isaiah simeone**

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\[ \huge{ x^{x^{x^{x^{x^{.^{.^.}}}}}}=2} \]

Find the value of \(x\) that satisfies the equation above.

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Anish Mukherjee**

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\[ \large \sqrt{12+\sqrt{12+\sqrt{12+\sqrt{12 + ...}}}}= \ ? \]

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math man**

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