Question

Oblicz przykład c i d
w c) powinno wyjść 12,5
w d) 0,05

Answer 1

C)
(6 - 11¹/²)(6 + 11¹/²)/[(√(6 - √11) - √(6 + √11)]² =
 = [6² - (11¹/²)²]/(√(6 - √11)² - 2[√(6 - √11)(√(6 + √11)] + √(6 + √11)²] =
= (36 - 11)/{6 - √11 - 2[√(6² - (√11)²] + 6 + √11] = 
= 25/[12 - 2√(36 - 11)] = 25/(12 - 2 * √25) = 25/(12 - 2 * 5) = 25/(12 - 10) = 
= 25/2 = 12,5
d)
[(3 - √5)¹/² + (3 + √5)¹/²]⁻² * [(27/8)¹/³ - 28°] =
= [(√(3 - √5) + √(3 + √5)]⁻² * [∛(27/8) - 1] =
= [3/2 - 1]/[√(3 - √5) + √(3 + √5)]² = 1/2 : {(3 - √5 + 2[√(3² - (√5))²] + 3 + √5} = 
= 1/2 : [6 + 2√(9 - 5)] = 1/2 : (6 + 2 * √4) = 1/2 : (6 + 4) = 1/2 : 10 = 
= 1/2 * 1/10 = 1/20 = 0,05