<s>[INST] Solve this question Question : $$\begin{align}a+b+c &= 0\\
a^3 +b^3 +c^3 &= 12\\
a^5 +b^5 +c^5 &= 40\end{align}$$
Then , $a^4 + b^4 + c^4 = ?$
My try : As a common perspective I just went to find any trick related to it and my first step is as usual as a common man will think
$3abc = 12$ and got $abc = 4$
After that I am unable to link it with any other equation
 [/INST] Hint: $$(a+b+c)^4=a^4+b^4+c^4+4a^3(b+c)+4b^3(a+c)+4c^3(a+b)+6(a^2b^2+b^2c^2+c^2a^2)+12abc(a+b+c)=0$$
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