Plz answer:

If 1＜=a＜=2, then will the following be true?

sqrt [a+2sqrt(a-1)] + sqrt [a-2sqrt(a-1)] = 2

Thanks.

Yes it holds.Sqrt (a+2sqrt(a-1))+sqrt(a-2sqrt(a-1))=2Squaring both sides,a+2sqrt(a-1)+a-2sqrt ( a-1)+ 2sqrt[(a+2sqrt(a-1))(a-2sqrt (a-1))]=42a+2sqrt{a^2-4a+4}=4a(+-)(a-2)=2Taking +ve value satisfies as a=2Taking-ve value satisfies as 2=2