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樓主 |
發表於 2004-9-10 19:58:49
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顯示全部樓層
Let x1 and x2 be the roots of the quiadratic equation x2-2tx+1=0 where -1<=t<=1
Define fn(t)=1/2(x1n+x2n) for n=0,1,2,3….
a).show that for n>=1,
fn+1(t)=2tfn(t)-fn-1(t).
b).hence,or otherwise,deduce that fn(t) is a polynomial in t ,of degree n and with leading coefficient 2n-1
n+1 ar.
n ar全部係 base黎. |
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