If a +b+c =0 and a^2+b^2+c^2 =1 , then the value ofa^4+b^4+c^4 is?

1 Answer
Mar 11, 2017

1/2

Explanation:

(a+b+c)^2=a^2+b^2+c^2+2(ab+ac+bc)=0 so

ab+ac+bc=-1/2

(a^2+b^2+c^2)^2=a^4+b^4+c^4+2(a^ 2b^2+a^2c^2+b^2c^2)=1 so

a^4+b^4+c^4=1-2(a^ 2b^2+a^2c^2+b^2c^2) but

(ab+ac+bc)^2=a^ 2b^2+a^2c^2+b^2c^2+2(a^2bc+ab^2c+abc^2) = 1/4

and consequently

a^ 2b^2+a^2c^2+b^2c^2 = 1/4-2(a+b+c)abc = 1/4

Finally

a^4+b^4+c^4=1-2/4=1/2