Question

solve for x : (3√x)^7 = 9261​

Answer 1

Factoring:  x3-9261 

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into

              (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

            a3+a2b+ab2-ba2-b2a-b3 =

            a3+(a2b-ba2)+(ab2-b2a)-b3 =

            a3+0+0+b3 =

            a3+b3

Check :  9261  is the cube of   21 

Check :  x3 is the cube of   x1

Factorization is :

             (x - 21)  •  (x2 + 21x + 441)