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本题难度不是很大,解题的入口宽,可以从多角度,多思路求解,是一道考查学生的基础知识和运用已学的知识分析问题和解决问题的佳题,本题还较好地渗透了数学思想和数学方法的应用,下面是本人从中探索出的七种解方法,希望喜欢题目已知a,b∈R+且有a+b=4,试证明:(a+3)2+(b+3)2≥50探索一:利用判别式令(a)+32+(b+3)2=y,∵a+b=4,∴a=4-b代入(a+3)2+(b+3)2=y化简整理有:2b2-8b+58-y=0该方程关于b的一元二次方程有实数根,故有:
The difficulty of this question is not great, wide entrance to the problem-solving, from a multi-angle, multi-thinking solution is a test of students’ basic knowledge and knowledge of the use of knowledge has been analyzed and problem-solving problems, the problem is better infiltrated Mathematical thinking and mathematical methods, the following is the seven solutions I have explored, I hope like a subject known a, b ∈ R + and a + b = 4, try to prove: (a +3) 2+ (b +3) 2 ≧ 50 Explicit 1: (a + 3) 2 + (b + 3) 2 = y, ∵a + b = 4 and ∴a = b + 3) 2 = y Simplification has: 2b2-8b + 58-y = 0 The equation on the b quadratic equation has a real root, it is: