Ta có: \(\left(a+b+c\right)^2=a^2+b^2+c^2+2\left(ab+bc+ca\right)=0\)
\(\Rightarrow2\left(ab+bc+ca\right)=-2017\)
\(\Rightarrow ab+bc+ca=\dfrac{-2017}{2}\)
\(\Rightarrow\left(ab+bc+ca\right)^2=1017072,25\)
\(\Rightarrow\left(ab\right)^2+\left(bc\right)^2+\left(ca\right)^2+2abc\left(a+b+c\right)=1017072,25\)
\(\Rightarrow a^2b^2+b^2c^2+c^2a^2=1017072,25\)
Ta có: \(\left(a^2+b^2+c^2\right)^2=a^4+b^4+c^4+2\left(a^2b^2+b^2c^2+c^2a^2\right)=2017^2\)
\(\Rightarrow a^4+b^4+c^4+2.1017072,25=2017^2\)
\(\Rightarrow a^4+b^4+c^4=3051216,75\)
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