题若a,b∈(0,1),求证:a2+b2+a2+(1-b)2+(1-a)2+b2+(1-a)2+(1-b)2≥2 2.这是一道散见于各种数学刊物上的不等式证明题.本题证明的方法很多,可以结合不等式的结构特点,利用分析法去证明,但过程较复杂;也可以打破思维定势,大胆联想,通过构造的方式,用数形结合法去证明,但解题方法 If a, b∈(0,1), verify: a2+b2+a2+(1-b)2+(1-a)2+b2+(1-a)2+(1-b)2≥2 2 This is a proof of inequality that can be seen in a variety of mathematical journals. There are many ways to prove this problem, which can be combined with the structural features of inequalities to use analytical methods to prove, but the process is more complex; it can also break the mindset, bold associations, Through the way of construction, using the method of combination of number and shape to prove, but the method of solving problems