Verified answer

E = 5 / (⁶√16 + ⁶√196 + ∛49)

E = 5 / (⁶√2⁴ + ⁶√14² + ∛49)

E = 5 / (∛2² + ∛14 + ∛49)

E = 5 / (∛4 + ∛14 + ∛49)

(∛a + ∛b + ∛c) . (∛a² + ∛b² + ∛c² - ∛ab - ∛ac - ∛bc) = a + b + c - 3∛abc ⇒Aplicando

E = 5 . [∛4² + ∛14² + ∛49² - ∛(4 . 14) - ∛(4 . 49) - ∛(14 . 49)] / (∛4 + ∛14 + ∛49) . [∛4² + ∛14² + ∛49² - ∛(4 . 14) - ∛(4 . 49) - ∛(14 . 49)]

E = 5 . [∛(2³ . 2) + ∛14² + ∛(7³ . 7) - ∛(2³ . 7) - ∛196 - ∛686] / (4 + 14 + 49 - 3∛(4 . 14 . 49)

E = 5 . (2∛2 + ∛14² + 7∛7 - 2∛7 - ∛14² - ∛686) / (67 - 3∛2744)

E = 5 . [2∛2 + 7∛7 - 2∛7 + ∛14 - ∛14 - ∛(7³ . 2)] / [67 - 3∛(7³ . 2³)]

E = 5 . (2∛2 + 7∛7 - 2∛7 - 7∛2) / (67 - 3 . 7 . 2)

E = 5 . (7∛7 - 2∛7 + 2∛2 - 7∛2) / (67 - 42)

E = 5 . (5∛7 - 5∛2) / 25

E = 5 . 5 . (∛7 - ∛2) / 25

E = 25 . (∛7 - ∛2) / 25

E = ∛7 - ∛2

Alternativa c)

16^(1/6) + 196^(1/6) + 49^(1/3) = 2^(2/3) + 2^(1/3)*7^(1/3) + 7^(2/3)

a = (2^(2/3) + 2^(1/3)*7^(1/3) + 7^(2/3))*7^(1/3) = 2^(2/3)*7^(1/3) + 2^(1/3)*7^(2/3) + 7)

b = (2^(2/3) + 2^(1/3)*7^(1/3) + 7^(2/3))*2^(1/3) = 2 + 2^(2/3)*7^(1/3) + 7^(2/3)*2^(1/3)

a - b = 7 - 2 = 5

resposta 7^(1/3) - 2^(1/3) (C)

pronto