已知实数a、b、c满足(a-b)开三次方+(b-c)开三次方=2,a-c=26,则a-2b+c=_____
问题描述:
已知实数a、b、c满足(a-b)开三次方+(b-c)开三次方=2,a-c=26,则a-2b+c=_____
答
令 x=(a-b)开三次方,y=(b-c)开三次方,则x+y=2,a-c=(a-b)+(b-c)=x^3+y^3=26,即x^3+y^3=(x+y)^3-3xy(x+y)=8-6xy=26,得xy=-3,联立x+y=2,解之得x=3,y=-1,或x=-1,y=3a-2b+c=(a-b)-(b-c)=x^3-y^3当x=-1,y=3,a-2b+c=x...