(1+√2013(√2012-√2011))/(√2011+√2012+√2013)+√2011

题目

(1+√2013(√2012-√2011))/(√2011+√2012+√2013)+√2011
简便运算,

答案

(1+√2013(√2012-√2011))/(√2011+√2012+√2013)+√2011
=[(√2012)²-(√2011)²+√2013(√2012-√2011)]/(√2011+√2012+√2013)+√2011
=[(√2012-√2011)(√2012+√2011)+√2013(√2012-√2011)]/(√2011+√2012+√2013)+√2011
=(√2012-√2011)(√2012+√2011+√2013)/(√2011+√2012+√2013)+√2011
=√2012-√2011+√2011
=√2012
把分子的1化成,(√2012)²-(√2011)²
再用公式:a²-b²=(a-b)(a+b)
然后分子分母约分.