Math Problem Find all solutions of the equation

Question

x^2/3 - 5x^1/3 = 36

Answer 1

First, let's subtract 36 from both sides of the equation.

 

x^2/3 - 5x^1/3 - 36 = 0

 

This polynomial can be factored. It is similar to x² - 5x - 36 = (x + 4)(x - 9)

 

(x^1/3 + 4)(x^1/3 - 9) = 0

 

Now, set each factor equal to 0 and solve for x.

 

x^1/3 + 4 = 0

 

x^1/3 = -4

 

x = -64 (we raised both sides of the equation to the third power)

 

x^1/3 - 9 = 0

 

x^1/3 = 9

 

x = 729

 

The solutions are -64 and 729