If n>0 and _ x 0 ((a-n) n x- x) n x x^2 =0 , then minimum value of a is

Step-by-step solution

aligned & _ x 0 ((a-n) n x- x) n x x^2 =0 & _ x 0 [ (a-n) n x- x x ] _ x 0 n x n x n=0 & n [ _ x 0 (a-n) n x x - _ x 0 x x ] _ n x 0 n x n x =0 . & n[(a-n) n-1] 1=0 & (a-n) n=1 & [ n 0] & a= 1 n +n & a= n^2+1 n & aligned a is minimum when n is minimum. The minimum value of n is 1 a= I +1 l =2