<s>[INST] How I can find the value of $abc$ using the given equations? If I have been given the value of 
$$\begin{align*}
a+b+c&= 1\\
a^2+b^2+c^2&=9\\
a^3+b^3+c^3 &= 1
\end{align*}$$
Using this I can get the value of 
$$ab+bc+ca$$
How i can find the value of $abc$ using the given equations?
I just need a hint.
I have tried by squaring the equations.
But could not get it.
Thanks in advance.
 [/INST] First $\displaystyle{(a+b+c)^2 = (a^2+b^2+c^2)+2(ab+bc+ca)}$, which implies $1 = 9+2X$ where $X=(ab+bc+ca) \implies (ab+bc+ca)=-4$
Using $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$, and substituting the known values  $1-3Y = 9+4$ and solve for $Y=abc$
Note: You can always check with Wolfram Alpha if your answer is correct (not to solve your problem) Check http://tinyurl.com/7n6ey2t
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