Question

Cube root of 38 +17root5

Answer 1

cube root:    a+ b √5 

38 + 17√5 =  a³ + b³ 5√5 + 3 a² b √5 + 3 a b² 5

a³ + 15 a b² = 38       =>  b² = (38 - a³) /15a

5 b³ + 3 a² b = 17
b (5 b² + 3 a²) = b (38 - a³ + 9 a³)/3a  = 17
b = 51a/(8a³ + 38)

substituting in the first equation...we get 
   51² a³ * 15  = (8 a³ + 38)² (38 - a³)
   Let a³ = x

so :  39015 x = (64 x² + 38² + 608 x) (38 - x)
                      = - 64 x³ + 38³ + (64*38 - 608) x² + (608*38 - 38²) x
       64 x³ - 1824 x² + 17355 x - 54872 = 0

solving this:   we get  x =  8
       so a = ∛8 = 2

so   b = 51*2/(102) = 1

answer:  cube root =   2 + √5

Answer 2

Answer:

Step-by-step explanation: