Question

已知a+b=根号下根号2012+根号2011,a-b=根号下根号2012-根号2011,求:(a·b)²的值

Answer 1

ab=［（a+b）²-（a-b）²］/4=根号2011/2

(a·b)²=2011/4

Answer 2

两边平方
a²+2ab+b²=√2012+√2011
a²-2ab+b²=√2012-√2011

相减
4ab=2√2012=4√503
ab=√503
所以原式=503