a+b+c = 0 \(\Leftrightarrow\left(a+b+c\right)^2=0\)\(\Leftrightarrow a^2+b^2+c^2+2ab+2bc+2ac=0\)
\(\Leftrightarrow a^2+b^2+c^2+2\left(ab+bc+ca\right)=0\)
\(\Leftrightarrow14+2\left(ab+bc+ca\right)=0\)
\(\Leftrightarrow ab+bc+ca=-7\) \(\Rightarrow\left(ab+bc+ca\right)^2=49\)
\(\Leftrightarrow a^2b^2+b^2c^2+c^2a^2+2ab^2c+2abc^2+2a^2bc=49\)
\(\Leftrightarrow a^2b^2+b^2c^2+c^2a^2+2abc\left(a+b+c\right)=49\)
\(\Leftrightarrow a^2b^2+b^2c^2+c^2a^2+2abc.0=49\)
\(\Leftrightarrow a^2b^2+b^2c^2+c^2a^2+0=49\) \(\Rightarrow a^2b^2+b^2c^2+c^2a^2=49\)
xét \(a^2+b^2+c^2=14\)\(\Rightarrow\left(a^2+b^2+c^2\right)^2=196\)
\(\Leftrightarrow a^4+b^4+c^4+2a^2b^2+2b^2c^2+2c^2a^2=196\)
\(\Leftrightarrow a^4+b^4+c^4+2.\left(a^2b^2+b^2c^2+c^2a^2\right)=196\)
\(\Leftrightarrow a^4+b^4+c^4+2.49=196\)
\(\Leftrightarrow a^4+b^4+c^4+98=196\)
\(\Rightarrow a^4+b^4+c^4=98\)
vậy giá trị của biểu thức B = \(a^4+b^4+c^4=98\)
