一、元素的互异性1例1.含有三个实数的集合可表示{a,b/a,1},也可表示为{a2,a+b,0},则a2007+b2007的值为()A.0 B.1 C.-1 D.±1解析:方法 1:集合{a,b/a,1}中含有1,因此集合{a2,a+b,0}中也含有1,若a2=1,则a=±1,当a=1时,集合{1,b,1}中两元素不互异,舍去.当a=1时,集合{-1,-b,1}与集合{1,b,-1,0}相等,得b=0,当a+b=1时,集合{a,b/a,1}={a2,1,0}这时b/a=0,即a=1,b=0与 First, the elements of the different sex 1 Example 1 contains a set of three real numbers can represent {a, b / a, 1}, can also be expressed as {a2, a + b, 0}, the value of a2007 + b2007 is ( ) A.0 B.1 C.-1 D. ± 1 Resolution: Method 1: The set {a, b / a, 1} contains 1, so the set {a2, a + b, 0} If a2 = 1, then a = ± 1, when a = 1, the set {1, b, 1} in the two elements are not mutually different, {A, b / a, 1} = {a2, 1, 0} when a + b = 1, b is equal to the set {1, b, -1,0} a = 0, ie a = 1, b = 0 and