## dinainjune 4 years ago how to solve this a^3>-1 and the answer is a<-1 , can anyone explain to me?

1. saifoo.khan

Yea!!

2. Ishaan94

a^3 > -1 a > -1

3. hahd

cube toot of a is?

4. Nick_Black

a^3>-1 a>-1

5. Ishaan94

toot !? lol

6. saifoo.khan

take cube root on both sides.

7. saifoo.khan

the cube root of -1 is -1.

8. hahd

ull end up with -1 again hence the answer

9. Nick_Black

no saif its -1

10. saifoo.khan

what nick?

11. Ishaan94

saif said the same

12. Nick_Black

-1^3=-1

13. saifoo.khan

Yea!

14. dinainjune

yes, it's cube root. and i still confuse

15. Ishaan94

or there is another way too a^3 > -1 a^3 +1 > 0 (a + 1)(a^2 + 1 -a)> 0 ^ ^ real complex a >-1

16. jim_thompson5910

a^3 > -1 a^3 + 1 > 0 (a+1)(a^2-a+1) > 0 .. factor with the sum of cubes formula Since a^2-a+1 is ALWAYS positive (look at the graph of a^2-a+1 to see this or complete the square on a^2-a+1), this means that a^2-a+1 has NO influence on the sign of the entire expression. So everything is dependent on the factor a+1 So because the entire expression is positive, and the sign depends on a+1, we know for sure that a+1 > 0 a+1 > 0 a > -1 So the solution is a > -1

17. Ishaan94

but I am sure you don't want the complex thing so just so a>-1

18. jim_thompson5910

make sure that there are no typos

19. Ishaan94

Good Job Jim

20. dinainjune

okay, thank you all :)