已知a+b+c=2 a2+b2+c2=3 a3+b3+c3=4求a4+b4+c4=？？

∵∴ ∵a+b+c=2 ∴4=(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac=3+2(ab+bc+ac) ∴ab+bc+ac=1/2 (1) ∵a+b+c=2 ∴8=(a+b+c)^3=a^3+b^3+c^3+3a^2 b+3ab^2+3a^2 c+3ac^2+3b^2 c+3bc^2+6abc =4+3a^2 b+3ab^2+3a^2 c+3ac^2+3b^2 c+3bc^2+6abc