標題: 關於Relationship between the Roots and Coefficients的問題 [打印本頁] 作者: wonderpiglet 時間: 28/9/2009 06:55 PM 標題: 關於Relationship between the Roots and Coefficients的問題 If A and B are the roots of the equation x^2-2x-6=0,find the values of A^2+2B A=alpha B=beta a=1,b=(-2),c=(-6) A+B=-b/a=2 AB=c/a=(-6) 請問怎計,我試過好多方法都不行?答案是10作者: simon199392 時間: 28/9/2009 08:34 PM 不就是solve equation 嗎... A+B=2 ---(1) AB=-6 ----(2) From (1), A=2-B ----(3) Subst (3) into (2) (2-B)B=-6 -B^2+2B=-6 B^2-2B-6=0 -(-2) +/- 開方(4+24) B=------------------------------- 2 B=1+/-開方7
So, B=1-開方7 { or A=1+開方7
A=1-開方7 { B=1+開方7 So, by using the result, A^2 +2B =(1-開方7)^2 + 2(1+開方7) =1-2開方7+7+2+2開方7 =1+7+2 =10 Or A^2 +2B =(1+開方7)^2 + 2(1-開方7) =1+2開方7+7+2-2開方7 =1+7+2 =10