The number of distinct solutions of the equations x¹¹-x^7+x^4-1=0 is

Step-by-step solution

Given equation is aligned & x¹¹-x^7+x^4-1=0 & =x^7 (x^4-1 )+1 (x^4-1 )=0 & = (x^4-1 ) (x^7+1 )=0 aligned Case (i): x^4-1=0 aligned & or x ^4=1 & x ^4=( O + i o ) & x ^4=( 2 k +i 2 k ) & x =( 2 k +i 2 k )^ 1 / 4 & ~K =0,1,2,3 aligned Case (ii): x^7+1=0 aligned & x ^7=-1= + i & x ^7= (2 k + )+ i (2 k + ) & x =( (2 k + )+ i (2 k + ))^ 1 / 7 & x = c is (2 k +1)^ / 7 & k =0,1,2,3,4,5,6 aligned now values of x are c is o =1, c is 3 2