初二数学题已知ａ+ｂ+c=0,a^2+b^2+c^2=1,求a^
已知ａ+ｂ+c=0,a^2+b^2+c^2=1,求a^4+b^4+c^4的值
ａ+ｂ+c=0 平方后 ==> ab + bc + ac = -0.5 再平方后 ==> ab^2 + bc^2 + ac^2 =1/4 a^2+b^2+c^2=1 ==> (a^2+b^2+c^2)^2=1 即 a^4 + b^4 + c^4 + 2[ab^2 + bc^2 + ac^2] = 1 ==> a^4+b^4+c^4 = 1/2