已知f(x)是四次多项式,且满足f(i)=1/i ,i=1,2,3,4,5,求f(6)的值
问题描述:
已知f(x)是四次多项式,且满足f(i)=1/i ,i=1,2,3,4,5,求f(6)的值
答案不是1/6
答
f(6)=-7/4设f(x)=ax^4+bx³+cx²+dx+e,依题意有:f(1)=a+b+c+d+e=1 (1)f(2)=16a+8b+4c+2d+e=1/2 (2)f(3)=81a+27b+9c+3d+e=1/3 (3)f(4)=256a+64b+16c+4d+e=1/4 (4)f(5)=625a+125b+25c+5d+e=1/5 (5)(5)-(4),(4...