Question

Find the minimal polynomial of = 2¹/³ - 4¹/³ over ℚ. Note that this is the lowest degree non-zero monic polynomial (x)∈ℚ[x] where ()=0

Answer 1

The minimal polynomial of ∛2 - ∛4 over ℚ can be found by completing the square.

Step-by-step explanation:

The minimal polynomial of ∛2 - ∛4 over ℚ can be found by applying the concept of completing the square. We start by simplifying the expression as 2x - x3. Then, we can complete the square in x2 to obtain (2x)² = 4(1 - x)². By taking the square root of both sides and rearranging the equation, we get the quadratic equation x² + 1.2x - 6.0 × 10-3 = 0.