Ta có : \(a+b+c=0\)
\(\Rightarrow\left(a+b+c\right)^2=0\)
\(\Rightarrow a^2+b^2+c^2+2\left(ab+bc+ca\right)=0\)
Mà \(a^2+b^2+c^2=18\)
\(\Rightarrow2\left(ab+bc+ca\right)=-18\)
\(\Rightarrow ab+bc+ca=-18:2=-9\)
\(\Rightarrow a^2b^2+b^2c^2+a^2c^2+2bc\left(a+b+c\right)=81\)
\(a^2b^2+a^2c^2+b^2c^2=81\)
Mặt khác : \(a^2+b^2+c^2=18\)
\(\Rightarrow a^4b^4+b^4c^4+a^4c^4+2\left(a^2b^2+b^2c^2+c^2a^2\right)=18^2=324\)
\(\Rightarrow a^4+b^4+c^4+2.81=324\)
\(\Rightarrow a^4+b^4+c^4=324-162=162\)
\(M=a^2\left(1-a^2\right)+b^2\left(1-b^2\right)+c^2\left(1-c^2\right)\)
\(=a^2+b^2+c^2-\left(a^4+b^4+c^4\right)\)
Mà : \(a^2+b^2+c^2=18\)
\(a^4+b^4+c^4=162\)
\(\Rightarrow M=18-162=-144\)
Vậy : .......
