Let [x] denote the largest integer x . If the number of solutions of x 4 ^2 x = 2+x-[x] 1-x+[x] is k , then for x [ 4 , 3 ] , the value of k^ ^2 x

Step-by-step solution

Given, x 4 ^2 x = 2+x-[x] 1-x+[x] aligned & x 4 ^2 x = 2+ x 1- x [ x-[x]= x ] & 2 x| x|= 2+ x 1- x =y( let ) & y= 2+ x 1- x >0 aligned [because x [0,1) , so 2+ x and 1- x are positive ] | x|= x, x [ 4 , 3 ] So, 2 x x= 2+ x 1- x Maximum value of 2 x x= 2 x is ' 1 '. and minimum value of 2+ x 1- x ( at x =0) is ' 2 '. For the given equation number of solution k=0 x [ 4 , 3 ], K^ ^2 x =0