Algebra
# Radical Expressions and Equations

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 $a+b$.