Algebra
# Algebraic Manipulation

\[S = \displaystyle\sqrt{9 - \sqrt{\dfrac{13}{9} + \sqrt{\dfrac{13}{81} - \sqrt{\dfrac{13}{6561} + \sqrt{\dfrac{13}{43046721} - .......}}}}}\]

If \(S = \sqrt{\dfrac{a}{b}}\) where \(a, b\) are both primes, find \(a + b\).

\[\large 2016^{x}+2016^{-x}=3\]

\[\large \sqrt{\frac{2016^{6x}-2016^{-6x}}{2016^{x}-2016^{-x}}} = \, ?\]

\[ \large {\begin{cases} x+y+z&=15 \\ xy+yz+xz&=72 \end{cases} } \]

Let \(x,y,\) and \(z\) be real numbers satisfying the system of equations above.

Find the possible range of \(x\).

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