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What is t^3+216?

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2 Answers

You have two more complex solutions.

Use the sum of two cubes' formula,

t^3 + 216 = t^3 + 6^3 = (t+6)(t^2-6t+36) = 0

t + 6 = 0 => t = -6

or

t^2-6t+36 = 0

=> t^2-6t = -36

=> (t-3)^2 = 9-36 = -27

t = 3 +/- 3sqrt(3) i

t3 + 216 = 0

Isolate the variable.

t3 = -126

Now take the cube root of each side, since the cube root of a number is the inverse of a number cubed.

√(t3) = √(-216) = -6

t = -6

Since (-6)(-6)(-6) = (-6)^3 = -216

Comments

Yes, the second factorization from the sum of two cubes. Robert has correct my error above. As he pointed out, there should be two more complex solutions!