a+b+c=0,ab+bc+ac=-1/2求a^4+b^4+c^4=

Question

a+b+c=0,ab+bc+ac=-1/2 求a^4+b^4+c^4=

Answer 1

a+b+c=0,ab+bc+ac=-1/2
（a+b+c）^2=a^2+b^2+c^2+2(ab+bc+ac)=a^2+b^2+c^2-1=0
a^2+b^2+c^2=1
a^4+b^4+c^4
=(a^2+b^2+c^2)^2-2(a^2b^2+b^2c^2+a^2c^2)
=1-2[(ab+bc+ac)^2-2abc(a+b+c)]
=1-2[(-1/2)^2-0]
=1-1/2
=1/2