Çöz ... 5 - x = sqrt (x + sqrt (x + sqrt (x + sqrtx)))) Bulmak x?

Cevap:

Cevap # = 5-sqrt5 #

Açıklama:

let • y = sqrt (x + sqrt (x + sqrt (x + sqrt (x + ….)))) #

Gönyeleme, • y ^ 2 = x + sqrt (x + sqrt (x + sqrt (x + sqrt (x + ….)))) #

• y ^ 2 = x + y #

Gibi, • y = 5-x #

• y ^ 2 = x + 5-X = 5 #

#y = + - sqrt5 #

Bu nedenle, • y ^ 2 = x + y #

# 5 = x + sqrt5 #

# X = 5-sqrt5 #