初中二次根式 计算题——(“根号2” -1）^2009×(“根号2”+1）^2010的结果是?
问题描述：
初中二次根式 计算题——(“根号2” -1）^2009×(“根号2”+1）^2010的结果是?
答
=（根号2” -1）乘以（根号2” -1）乘以......乘以（“根号2”+1）乘以......
=（“根号2”+1）乘以（“根号2” -1）乘以......（2009个）乘以(“根号2”+1）
根据公式（a+b)乘以（a-b)=a²+b²
=1乘以（“根号2”+1）=“根号2”+1
答
原式=(√2-1)^2009×(√2+1)^2009×(√2+1)
=[(√2-1)×(√2+1)]^2009×(√2+1)
=[(√2)²-1²]^2009×(√2+1)
=1^2009×(√2+1)
=√2+1