# Math Help - Difference of cubes

1. ## Difference of cubes

Find all solutions of the following equation. (If there are more answer boxes than answers, enter NONE in the extra boxes.) a3x3 + 1000 = 0
x = 1
(real solution)
x = 2
(smaller imaginary part)
x = 3
(larger
I was able to figure out part one and for 2 and 3 this is what i came up with but they are incorrect.

2. Originally Posted by tmac11522
Find all solutions of the following equation. (If there are more answer boxes than answers, enter NONE in the extra boxes.) a3x3 + 1000 = 0
x = 1
(real solution)
x = 2
(smaller imaginary part)
x = 3
(larger
I was able to figure out part one and for 2 and 3 this is what i came up with but they are incorrect.
The last two cannot be solutions as they contain $x$.

.

3. Originally Posted by tmac11522
Find all solutions of the following equation. (If there are more answer boxes than answers, enter NONE in the extra boxes.) a3x3 + 1000 = 0
x = 1
(real solution)
x = 2
(smaller imaginary part)
x = 3
(larger
I was able to figure out part one and for 2 and 3 this is what i came up with but they are incorrect.
ditto to what Constantine said

i assume by a3x3 you mean $a^3x^3$ ??

in that case, note that what you have is:

$(ax)^3 + 10^3 = 0$

you can use the sum of two cubes formula: $n^3 + m^3 = (n + m)(n^2 - nm + m^2)$

the first factor gave you the first solution. use the quadratic formula on the second factor to get the second solution. here your $n = ax$ and your $m = 10$