Given : ³√(x + 5) - ³√x = 1
We can write it in the simplest form as follows :
→(x+5) ^1/3 - (x)^1/3 -1 = 0
→ let u = ³√(x + 5) and x = u^3-5
Therefore:
u -³√u^3 -5
1. Then solve for u -³√u^3 -5=1
u = (3+ √57)/6 ...(1) and u = (3-√57)/6....(2)
2. Substitude u = ³√(x + 5) and solve :
(i) ³√(x + 5 = (3+ √57)/6
therefore x = -5/2 +(7√57)/18
(ii) ³√(x + 5 = (3- √57)/6
Therefore x = -5/2 +(7√57)/18
Therefore a = -5/2
b = 7
c =57
d = 18