dinainjune

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

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saifoo.khan

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Yea!!

Ishaan94

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a^3 > -1
a > -1

hahd

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cube toot of a is?

Nick_Black

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a^3>-1
a>-1

Ishaan94

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toot !? lol

saifoo.khan

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take cube root on both sides.

saifoo.khan

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the cube root of -1 is -1.

hahd

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ull end up with -1 again hence the answer

Nick_Black

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no saif its -1

saifoo.khan

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what nick?

Ishaan94

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saif said the same

Nick_Black

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-1^3=-1

saifoo.khan

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Yea!

dinainjune

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

Ishaan94

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

jim_thompson5910

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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

Ishaan94

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

jim_thompson5910

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make sure that there are no typos

Ishaan94

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Good Job Jim

dinainjune

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okay, thank you all :)