{a^2-bc-8a+7=0

题目

{a^2-bc-8a+7=0
{b^2+c^2+bc-6a+6=0
求a的取值范围.

答案

bc=a^2-8a+7
两式相减得
a^2-2bc-b^2-c^2-2a+1=0
(b+c)^2=(a-1)^2
b+c=±a-1
b,c是方程x^2±(a-1)x+a^2-8a+7=0的两根
Δ=(a-1)^2-4(a-1)(a-7)>=0
(a-1)(a-1-4a+28)>=0
(a-1)(27-3a)>=0
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