Kakšne so vrednosti x v enačbi x ^ (2/5) + x ^ (1/5) + 1 = 3?

Odgovor:

Obe rešitvi sta # x = 1 # in #-32#.

Naredite zamenjavo, da bo enačba lažje reševala:

# x ^ (2/5) + x ^ (1/5) + 1 = 3 #

# x ^ (2/5) + x ^ (1/5) -2 = 0 #

# (x ^ (1/5)) ^ 2 + x ^ (1/5) -2 = 0 #

Let # u = x ^ (1/5) #:

# u ^ 2 + u-2 = 0 #

# (u + 2) (u-1) = 0 #

# u = -2,1 #

Put # x ^ (1/5) # nazaj v # u #:

#barva (bela) {barva (črna) ((x ^ (1/5) = - 2, qquadquadx ^ (1/5) = 1), (x = (- 2) ^ 5, qquadquadx = (1) ^ 5), (x = -32, qquadquadx = 1):} #

To sta dve rešitvi. Upam, da je to pomagalo!