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

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Mathematics

Cristal Flowers

2 August, 09:38

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

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Orozco · 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)