Question

Which expressions represent solutions to the equation y^3 = 64?

A) -4, 4
B) -∛64, ∛64
C) -8, 8
D) -∛3, ∛3

Answer 1

The expressions that represent solutions to the equation y^3 = 64 are -∛64 and ∛64.

Step-by-step explanation:

The equation y^3 = 64 represents a cubic equation. To find the solutions, we can take the cube root of both sides of the equation. The cube root of 64 is 4, so one solution is y = 4. However, since this is a cubic equation, there can be three solutions. The other two solutions can be found by taking the complex cube roots of 64, which are -2 + 2i√3 and -2 - 2i√3. Therefore, the expressions that represent solutions to the equation y^3 = 64 are B) -∛64, ∛64.