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FindInstance what inspite ?


Who have idea what function uses inspite FindInstance in procedure?
\!\(FindInstance[Chop[N[Root[\(-1\) - 2\ #1 - 2\ #1\^2 - #1\^3 + #1\^5 
&, 2] \
+ Root[\(-1\) - 2\ #1 - 2\ #1\^2 - #1\^3 + #1\^5 &, 3], 500]] == a + b\
                Root[\(-1\) - 2\ #1 - 2\ #1\^2 - #1\^3 + #1\^5 &,
                     1] + c\ Root[\(-1\) - 2\ #1 - 2\ #1\^2 - #1\^3 + 
#1\^5 \
&, 1]^2 + d\
            Root[\(-1\) - 2\ #1 - 2\ #1\^2 - #1\^3 + #1\^5 &, 1]^3 + e\
                    Root[\(-1\) - 2\ #1 - 2\ #1\^2 - #1\^3 + #1\^5 &,
                   1]^4 && a != 0, {a, b, c, d, e}, Integers]\)
And anser is empty set {}
Good answer  is {a,b,c,d,e}={-2,-3,-2,-1,2}
Who know how I can realize that procedure in Mathematica ?

Best wishes
Artur




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