Question

已知实数a、b、c满足a+b+c=0,a^2+b^2+c^2=0.1,求a^4+b^4+c^4=?

题
要过程
答案是0.005

Answer 1

（一）a+b+c=0.===>b+c=-a.a^2+b^2+c^2=1/10.===>(b+c)^2+a^2=(1/10)+2bc.===>2a^2=(1/10)+2bc.===>bc=a^2-(1/20).===>b^2+c^2=(b+c)^2-2bc=a^2-2[a^2-(1/20)]=(1/10)-a^2.即有b^2+c^2=(1/10)-a^2.bc=a^2-(1/20).(二）原式=a^4+[b^2+c^2]^2-2(bc)^2=a^4+[(1/10)-a^2]^2-2[a^2-(1/20)]^2=1/200=0.005