<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] Hint
Use Newton’s identities and Vieta's formulas to find $a,b,c$ as roots of a degree 3 polynomial.
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