<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] Use $$(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$$
and $$a^3+b^3+c^3-3bc=(a+b+c)\{(a+b+c)^2-3(ab+bc+ca)\}$$  to find $ab+bc+ca=u, abc=v$(say)
So, $a,b,c$ are the roots of $$t^3-4t^2+ut-v=0$$
Use Newton's Sums
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