If x^ (2) - 2 = 2^ (2/3) + 2 (-2/3) prove that x = 2^ (1/3) + 2^ (-1/3)

Question

Mathematics

Andres

28 July, 20:07

If x^ (2) - 2 = 2^ (2/3) + 2 (-2/3) prove that x = 2^ (1/3) + 2^ (-1/3)

+1

Answers (1)

Know the Answer?

Aimee Johnson · Answer 1

Step-by-step explanation:

x² - 2 = 2^ (2/3) + 2^ (-2/3)

x² = 2^ (2/3) + 2 + 2^ (-2/3)

x² = (2^ (1/3)) ² + 2 * 2^ (1/3) * 2^ (-1/3) +

(2^ (-1/3)) ² (It is in the form of a²+2ab+b²)

x² = (2^ (1/3) + 2^ (-1/3)) ²

x = 2^ (1/3) + 2^ (-1/3)