Question

X^3+216=0 solve the equation , try your solutions

Answer 1

X³  + 216 = 0

x³   = 0 - 216

x³   = - 216    Take the cube root of both sides.

∛x³ =  ∛-216

x = -6


Check:

x³  + 216 = 0,    x = -6

(-6)³  + 216 = 0

-216 + 216 = 0

0  =  0          Correct.

Answer 2

 
 x = -6

Factoring:  x3+216   

A sum of two perfect cubes,  a3 + b3 can be factored in to: (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 :  216  is the cube of   6

Factorization is :
             (x - 6)  •  (x^2 + 6x + 36)

Hope This Helped