Môžete začať racionalizáciou:
(Sqrt (1 + x) + sqrt (1-x)) / (sqrt (1 + x) -sqrt (1-x)) x (sqrt (1 + x) + sqrt (1-x)) / (sqrt (1 + x) + sqrt (1-x)) =
= (Sqrt (1 + x) + sqrt (1-x)) ^ 2 / (2 x) =
= ((1 + x) + 2sqrt (1 + x) sqrt (1-x) + (1-x)) / (2 x) =
= (2 + 2sqrt (1-x ^ 2)) / (2 x) =
= (1 + sqrt (1-x ^ 2)) / (x) =
dosadením: X = sqrt (3) / 2 dostanete:
= (1 + sqrt (1- 3/4)) / (sqrt (3) / 2) = (1 + 1/2) * (2 / sqrt (3)) =
= 3/2 * 2 / sqrt (3) = 3 / sqrt (3) = 3 / sqrt (3) * sqrt (3) / sqrt (3) = sqrt (3)
Dúfam, že to je to, čo ste potrebovali!:-)
