I came across this problem from a post on instagram. $$x^4+y^4+z^4=32$$ $$x^5+y^5+z^5=186$$ $$x^6+y^6+z^6=803$$ $$(x+y+z) \;\;\; \epsilon \;\;\; N$$ $$x+y+z=?$$
My attempt: I set the following: $$x+y+z=a$$ $$xy+yz+za=b$$ $$xyz=c$$ $$$$Now I tried to express each equations in terms of $a,b,c$ and hence solve for but I end up with a huge mess and nothing works out. There are just too many terms in the expansion of $\;\; (x+y+z)^6$. There must be a better way out of this.
