标题: [数学] 2007-10-19 [打印本页]

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作者: 老猫    时间: 2007-10-19 06:48     标题: 2007-10-19

已知f(x)=x3+ax2+bx+c，f(1)=1,f(2)=2。求f(8)-f(-5).

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作者: lh312151    时间: 2007-10-19 12:18

f(1)=1+a+b+c=1,  a+b+c=0,  c=-a-b
f(2)=8+4a+2b+c=2, 4a+2b+c=-6, 4a+2b-a-b=-6, 3a+b=-6
f(8)=512+64a+8b+c
f(5)=-125+25a-5b+c
f(8)-f(-5)=637+39a+13b=637+13*(3a+b)=637-13*6=559.

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