化简:(根号2+1)^2014×(根号2-1)^2015
问题描述:
化简:(根号2+1)^2014×(根号2-1)^2015
答
(根号2+1)^2014×(根号2-1)^2015
=(根号2+1)^2014×(根号2-1)^2014×(根号2-1)
=【(根号2+1)×(根号2-1)】^2014×(根号2-1)
=【(根号2)²-1²】^2014×(根号2-1)
=(2-1)^2014×(根号2-1)
=1^2014×(根号2-1)
=1×(根号2-1)
=根号2-1