证明: 设x0,x1,...,xn是f(x)的n+1个互不相同的根则 f(xi) = 0, i=0,1,...,n即有a0+a1x0+a2x0^2+...+anx0^n = 0a0+a1x1+a2x1^2+...+anx1^n = 0 ... ...
... ...a0+a1xn+a2xn^2+...+anxn^n = 0.把a0,a1,...,an看作未知量, 上式即为n+1元齐次线性方程组.其系数行列式 =1x0x0^2 ... x0^n1x1x1^2 ... x1^n.........1xnxn^2 ... xn^n这是Vandermo...
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