Question

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

Answer 1

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)