※ 引述《hunter405 (呵呵)》之銘言:
: 5.設x^4-3x^3+5x^2+x+2=0的四根為a,b,c,d
: 則(2-a)^(-1)+(2-b)^(-1)+(2-c)^(-1)+(2-d)^(-1)=?
: 好像不難@
: 可是想不出來~
a, b, c, d are the roots of x^4-3x^3+5x^2+x+2
then
a-2(=u), b-2(=v) , c-2 (=s), d-2(=t)
are the roots of (x+2)^4-3(x+2)^3+5(x+2)^2+(x+2)+2
(x^4+5x^3+11x^2+17x+16)
then 1/u, 1/v 1/s, 1/t are the roots of
(1/x)^4+5(1/x)^3+11(1/x)^2+17(1/x)+16=0
that is, 16x^4+17x^3+11x^2+5x+11=0
-(1/u +1/v +1/s +1/t)=17/16
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