51²+49²用简便方法计算

题目

51²+49²用简便方法计算

答案

51" + 49"
= 51" - 1" + 1" + 49" - 1" + 1"
= (51 - 1)(51 + 1) + 1 + (49 + 1)(49 - 1) + 1
= 50 X 52 + 1 + 50 X 48 + 1
= 50 X (52 + 48) + 2
= 50 X 100 + 2
= 5002
或者
= (50 + 1)" + (50 - 1)"
= 50" + 1" + 2X50X1 + 50" + 1" - 2X50X1
= 2 X ( 50" + 1" )
= 2 X 2501
= 5002