若a=根号2+1分之1,则a的平方+2a+3等于?

问题描述:

若a=根号2+1分之1,则a的平方+2a+3等于?

a=根号2减1,结果得4

∵a=根号2+1分之1
∴a=√2-1
a²+2a+3=﹙a+1﹚²+2
=﹙√2+1-1﹚²+2
=2+2=4

a=1/﹙√2+1﹚=√2-1
a+1=√2
∴ a²+2a+3=﹙a+1﹚²+2=﹙√2﹚²+2=4.