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# Systems of Equations

Vieta root jumping is a descent method that occurs when you have to solve a Diophantine equation whose solutions have a recursive structure. Popular in advanced math olympiad number theory problems.

\[\begin{cases} { x }^{ 2 }+{ y }^{ 2 }=30 \\ x+y=10 \end{cases}\]

If the above equations are true simultaneously, then find the value of \(xy\).

\[ \large \begin{cases} { a(b+c)=32 } \\ { b(c+a) = 65 } \\ {c(a+b) = 77 } \end{cases}\]

Given that \(a , b,\) and \( c\) are positive real numbers that satisfy the system of equations above, find the value of \(abc\).

Note: These are not linear equations.

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