Oblicz :
(1,4)⁻⁵ * (⁵/₇) ⁻⁵ + 5 ½ * 5½ + 7½ * 7½
_______________________________ =
(3¹·⁵ - √7)(3¹·⁵ +√7)
(1,4 jest do potęgi -5, 5/7 też do -5, a 3 na dole do potęgi 1,5)
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(1,4)⁻⁵ * (⁵/₇) ⁻⁵ + 5 ½ * 5½ + 7½ * 7½
_______________________________ =
(3¹·⁵ - √7)(3¹·⁵ +√7)
Najpierw rozwiążmy licznik wyrażenia
(1,4)⁻⁵ * (⁵/₇) ⁻⁵ + 5 ½ * 5½ + 7½ * 7½ = (14/10)⁻⁵ * (5/7)⁻⁵ + 5½ + 5½ + 7½ * 7½ =
= (10/14)⁵ * (7/5)⁵ + (5½)² + (7½)² = (10/14 * 7/5)⁵⁺⁵ + 30¼ + 56¼ = (2/2)¹⁰ + 30¼ + 56¼ =
= 1 + 86½ = 87½
Następnie obliczamy mianownik
(3¹·⁵ - √7)(3¹·⁵ +√7) = (3¹ ⁵)² - 7 = 3³ - 7 = 27 - 7 = 20
Iloraz ma postać
87½/20 = 175/2 : 20 = 175/2 * 1/20 = 175/40 = 4,375