Sam claims that there is no maximum for the problem: xi ,( i is from 1 to n) subject to

xi = 1 . Prove or disprove his claim with necessary steps.

(b) Find the extremum of the quadratic form P( x1, x2, x3) = x1^2 + x2^2 + 2x3^2 - 2x1x2 + 4x1x3 + 4x2x3 subject to the constraint

xi^2= 1. (where i is from 1 to 3)