a: a+b+c=0
=>\(\left(a+b+c\right)^2=0^2=0\)
=>\(a^2+b^2+c^2+2\left(ab+ac+bc\right)=0\)
=>2(ab+ac+bc)=-2
=>ab+ac+bc=-1
=>\(\left(ab+ac+bc\right)^2=\left(-1\right)^2=1\)
=>\(a^2b^2+b^2c^2+a^2c^2+2a^2bc+2abc^2+2ab^2c=1\)
=>\(a^2b^2+b^2c^2+a^2c^2+2abc\left(a+b+c\right)=1\)
=>\(a^2b^2+b^2c^2+a^2c^2=1\)
\(\left(a^2+b^2+c^2\right)^2=2^2=4\)
=>\(a^4+b^4+c^4+2\left(a^2b^2+a^2c^2+b^2c^2\right)=4\)
=>\(a^4+b^4+c^4+2\cdot1=4\)
=>\(a^4+b^4+c^4=4-2=2\)
b: a+b+c=0
=>\(\left(a+b+c\right)^2=0^2=0\)
=>\(a^2+b^2+c^2+2\left(ab+ac+bc\right)=0\)
=>2(ab+ac+bc)=-1
=>ab+ac+bc=-1/2
=>\(\left(ab+ac+bc\right)^2=\left(-\frac12\right)^2=\frac14\)
=>\(a^2b^2+b^2c^2+a^2c^2+2a^2bc+2abc^2+2ab^2c=\frac14\)
=>\(a^2b^2+b^2c^2+a^2c^2+2abc\left(a+b+c\right)=\frac14\)
=>\(a^2b^2+b^2c^2+a^2c^2=\frac14\)
\(\left(a^2+b^2+c^2\right)^2=\left(-\frac12\right)^2=\frac14\)
=>\(a^4+b^4+c^4+2\left(a^2b^2+a^2c^2+b^2c^2\right)=\frac14\)
=>\(a^4+b^4+c^4+2\cdot\frac14=\frac14\)
=>\(a^4+b^4+c^4=\frac14-\frac12=-\frac14<0\) (vô lý)
=>\(a^4+b^4+c^4\) không có giá trị
