Odpowiedzi

2009-10-19T17:16:24+02:00
A) √(3 - 2√2) = 1/√(3 + 2√2)
L = [√(3 - 2√2)]/1 = [√(3 - 2√2) * √(3 + 2√2)]/[√(3 + 2√2)] = {√[(3 - 2√2)(3 + 2√2)]}/[√(3 + 2√2)] = {√[9 - 8]}/[√(3 + 2√2)] = 1/√(3 + 2√2) = P

b) √(2 + √3) = 1/√(2 - √3)
L = [√(2 + √3)]/1 = [√(2 + √3) * √(2 - √3)]/[√(2 - √3)] = {√[(2 + √3)(2 - √3)]}/[√(2 - √3)] = {√[4 - 3]}/[√(2 - √3)] = 1/√(2 - √3) = P

c) √(9 + 2√14) = √2 + √7
P = √(9 + 2√14) = √(√2 + √7 + 2√14) = √(√2 + √7)² = √2 + √7 = P

d) √(13-2√30) = √10 - √3
L = √(13 - 2√30) = √(√10 + √3 - 2√30) = √(√10 - √3)² = √10 - √3 = P