Re: [中學] 函數的交點
※ 引述《realkawaii (邱邱)》之銘言：
: 想請問大家一題
: 若一次函數y=m(x-2)+1與三次函數y=(x-2)^3+1的圖形，
: 有三個相異的交點A(a,b) B(c,d) C(2,1)，則a+b+c+d=?
: 麻煩大家求解
: 感謝!
=> m(x-2) + 1 = (x-2)^3 + 1
=> (x-2) [ (x-2)^2 - m ] = 0
=> 三根為 2 , a , c
由 根與係數關係 a + c = 4
b = m(a-2) + 1
d = m(c-2) + 1
b+d = m(a+c) - 4m + 2 = 2
=> a + b + c + d = 6
有錯還請不吝指正。
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If people do not believe that mathematics is simple,
it is only because they do not realize how complicated life is.
－ John von Neumann
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10/10 09:53, , 1F
10/10 09:53, 1F
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