(急)高一数学题由等式x*4+a1x*3+a2x*2+a3x+a4=(x+1)*4+b1(x+1)*3+b2(x+1)*2+b3(x+1)+b4定义映射f:(a1,a2,a3,a4)--b1+b2+b3+b4则f(4,3,2,1)=A:10B:7C:-1D:0

Question

(急)高一数学题由等式x*4+a1x*3+a2x*2+a3x+a4=(x+1)*4+b1(x+1)*3+b2(x+1)*2+b3(x+1)+b4 定义映射f:(a1,a2,a3,a4)--b1+b2+b3+b4 则f(4,3,2,1)=______ A:10 B:7 C:-1 D:0

Answer 1

x*4代表x的四次方吧，我习惯用x^4代表x的四次方。 (x+1)^4=(x^2+2x+1)^2=x^4+4x^2+1+2x^2×(2x)+2×x^2*1+2×(2x)×1 =x^4+4x^3+6x^2+4x+1 f(4,3,2,1)=x^4+4x^3+6x^2+2x+1=(x+1)^4-2x=(x+1)^4-2(x+1)+2 得b1=0，b2=0，b3=-2，b4=2 因f:(a1,a2,a3,a4)=b1+b2+b3+b4 f(4,3,2,1)=b1+b2+b3+b4=0+0+(-2)+2=0