设a、b、c满足a2-bc-8a+7 b2+c2+bc-6a+6=0 对满足方程组的任意a值,都有√(a+c)-a＞m成立,求m范围

题目

设a、b、c满足a2-bc-8a+7 b2+c2+bc-6a+6=0 对满足方程组的任意a值,都有√(a+c)-a＞m成立,求m范围
m为常数
快,

答案

①a²-bc-8a+7=0②b²+c²+bc-6a+6=0 ②-①得
(b+c)^2=(a-1)^2
又根据bc=a^2-8a+7-(a-1)^2/4 解得1