Answer:
x = -(7/2)^(1/6) or x = (7/2)^(1/6) or x = -(-1)^(1/3) (7/2)^(1/6) or x = (-1)^(1/3) (7/2)^(1/6) or x = -(-1)^(2/3) (7/2)^(1/6) or x = (-1)^(2/3) (7/2)^(1/6)
Explanation:
Solve for x:
2 x^6 - 7 = 0
Add 7 to both sides:
2 x^6 = 7
Divide both sides by 2:
x^6 = 7/2
Taking 6^th roots gives (7/2)^(1/6) times the 6^th roots of unity:
Answer: x = -(7/2)^(1/6) or x = (7/2)^(1/6) or x = -(-1)^(1/3) (7/2)^(1/6) or x = (-1)^(1/3) (7/2)^(1/6) or x = -(-1)^(2/3) (7/2)^(1/6) or x = (-1)^(2/3) (7/2)^(1/6)