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# Radical Expressions and Equations

Combine your skills of working with exponents and manipulating expressions for radical glory.

Determine the sum of all possible integer values of \(x<100\) such that \(y\) is an integer.

\(\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x...}}}}=y\)

\[x-\sqrt{\frac{x}{2}+\frac{7}{8}-\sqrt{\frac{x}{8}+\frac{13}{64}}}=179\]

Find the value of \(10x\).

\[ \Large{\frac1{\sqrt[3]{1}+\sqrt[3]{2}+\sqrt[3]{4}} + \frac1{\sqrt[3]{4}+\sqrt[3]{6}+\sqrt[3]{9}} + \frac1{\sqrt[3]{9}+\sqrt[3]{12}+\sqrt[3]{16}}} \]

If the expression above can be simplified to the form of \({\sqrt[3] a + b} \) for integers \(a\) and \(b\), find the value of \(a+b\).

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