Need help solving a particular system of non-linear equations analytically How would one go about analytically solving a system of non-linear equations of the form:
$a + b + c = 4$
$a^2 + b^2 + c^2 = 6$
$a^3 + b^3 + c^3 = 10$
Thanks!

Hint: Newton's identities.
$$\begin{align*}a+b+c&=4\\ ab+bc+ca=\frac12((a+b+c)^2-(a^2+b^2+c^2))&=\frac12(4^2-6)=5\\abc=\frac13((ab+bc+ca-a^2-b^2-c^2)(a+b+c)+(a^3+b^3+c^3))&=\frac13((5-6)\cdot 4+10)=2\end{align*}$$
Remember that $a,\ b,\ c$ are the three roots of a polynomial $P(t)=(t-a)(t-b)(t-c)=t^3-(a+b+c)t^2+(ab+bc+ca)t-abc$.
