Có:
\(a+b+c=0\)
\(\Rightarrow\left(a+b+c\right)^2=0\)
\(\Rightarrow a^2+b^2+c^2=-2\left(ab+bc+ac\right)\)
\(\Rightarrow\left(a^2+b^2+c^2\right)^2=4\left(ab+bc+ac\right)^2\)
\(\Rightarrow a^4+b^4+c^4+2\left(a^2b^2+b^2c^2+a^2c^2\right)=2\left[a^2b^2+b^2c^2+a^2c^2+abc\left(a+b+c\right)\right]\)
\(\Rightarrow a^4+b^4+c^4=2\left(a^2b^2+b^2c^2+a^2c^2\right)\)
\(\Rightarrow a^4+b^4+c^4+1=2\left(a^2b^2+b^2c^2+a^2c^2\right)+1\)
Có:
\(\left(a^2+b^2+c^2\right)^2=4\left(ab+bc+ac\right)^2\)
\(\Rightarrow4\left(ab+bc+ac\right)^2=196\)
\(\Rightarrow\left(ab+bc+ac\right)^2=49\)
\(\Rightarrow a^2b^2+b^2c^2+a^2c^2=49\)
\(\Rightarrow a^4+b^4+c^4+1=2\left(a^2b^2+b^2c^2+a^2c^2\right)+1\)
\(\Rightarrow a^4+b^4+c^4+1=2.49+1\)
\(\Rightarrow a^4+b^4+c^4+1=99\)
