Solve Using Substitution. Show solution please ☺️

Question

r^2/3+8r^1/3=-15

Answer 1

(r^1/3)² + 8(r^1/3) + 15 = 0

 

where      q = r^1/3              and              q³ = r

 

Then,

 

q² + 8q + 15 = 0

 

 

Solve quadratic equation for q.

Answer 2

r^2/3 + 8r^1/3 = -15

 

Let x = r^1/3

 

x² + 8x = -15

 

x² + 8x + 15 = 0

 

(x + 5)(x + 3) = 0

 

x = -3 or -5

 

If x = -3,

 

r^1/3 = -3 ⇒ r = -27

 

If x = -5,

 

r^1/3 = -5 ⇒ r = -125