<s>[INST] If $a+b+c = 4, a^2+b^2+c^2=7, a^3+b^3+c^3=28$ find $a^4+b^4+c^4$ and $a^5+b^5+c^5$ I have tried to solve it but cannot find any approach which would lead me to the answer
 [/INST] Maple:
simplify(a^4+b^4+c^4, {a+b+c = 4, a^2+b^2+c^2 = 7, a^3+b^3+c^3 = 28}) = 209/2
simplify(a^5+b^5+c^5, {a+b+c = 4, a^2+b^2+c^2 = 7, a^3+b^3+c^3 = 28}) = 334
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