Question 11
(GDR 1) Given real numbers $x_1,x_2,\ldots,x_n$ ($n\ge2$), with $x_i\ge1/n$ ($i=1,2,\ldots,n$) and with $x_1^2+x_2^2+\cdots+x_n^2=1$, find whether the product $P=x_1x_2x_3\cdots x_n$ has a greatest and/or least value and if so, give these values.