Jika x = sqrt3 / 2 maka {sqrt (1 + x) + sqrt (1-x)} / {sqrt (1 + x) - sqrt (1-x)}?

Anda boleh bermula dengan merasionalisasi:

(sqrt (1 + x) + sqrt (1-x)) / (sqrt (1 + x) -sqrt (1-x) sqrt (1 + x) + sqrt (1-x)) = #

# = (sqrt (1 + x) + sqrt (1-x)) ^ 2 / (2x) = #

# = ((1 + x) + 2sqrt (1 + x) sqrt (1-x) + (1-x)) / (2x) = #

# = (2 + 2sqrt (1-x ^ 2)) / (2x) = #

# = (1 + sqrt (1-x ^ 2)) / (x) = #

Penggantian: # x = sqrt (3) / 2 # anda mendapatkan:

# = (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)

Semoga ia adalah apa yang anda perlukan!:-)