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