Question

If 12p + 1 is the cube of a positive integer, where p is a positive odd integer, find 3√12p + 1

Answer 1

Let

x³ = 12p + 1 

12p = x³ - 1

  p   = (x³ - 1)/12


We get p to be a cube when we make x = 8

p = (8³ - 1)/12

   = 18


2p + 1 = 12(18) + 1

           = 217


∛12p + 1 = ∛217 = 6

Answer 2

Answer:

Step-by-step explanation:

Let

x³ = 12p + 1

12p = x³ - 1

p = (x³ - 1)/12

We get p to be a cube when we make x = 8

p = (8³ - 1)/12

= 18

2p + 1 = 12(18) + 1

= 217

∛12p + 1 = ∛217 = 6