【用戶】Kimilce Ro
【年級】高三下
【評論內容】a, b, c是三根,那就(x-a)(x-b)(x-c)=x^3-3x^2+4x-1=0=x^3-(a+b+c)x^2+(ab+bc+ac)x-abc=x^3-3x^2+4x-1=0,由此可知,a+b+c=3,ab+bc+ac=4,abc=1,由此可知,c是對的,由上面導-a, -b,-c=(x+a)(x+b)(x+c)=x^3+(a+b+c)x^2+(a+b+c)x^2+abc=0a對,(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca=9=a2 + b2 + c2 + 2ab + 2bc + 2ca=2*4+a2 + b2 + c2,a2 + b2 + c2=1b不對,(a+b+c)(a2 + b2 + c2 - ab - bc - ca) = a3 + b3 + c3 - 3abc=3*(1-4)=a3 + b3 + c3 -3*1,a3 + b3 + c3=-6d無法求證5,既然是3根,餘式應為常數或...