Solve the equation after making an appropriate substitution:

Question

X⁶-511x³=512

 

Determine the appropriate substitution using the new variable u:u = 

 

Write new quadric equation using variable u: 

 

Solvery the new quadratic equation for the variable u. u = 

 

The solution set to the original equation is: 

Answer 1

x^{6 _} 511x³ - 512 = 0

 

(x³)² - 511(x³) - 512 = 0

 

Let u = x³   Then, u² - 511u - 512 = 0

 

                         (u - 512)(u + 1) = 0

 

u = 512 or u = -1

 

So, x³ = 512 or x³ = -1

 

x = (512)^1/3 or x = -1

 

x = 8 or x = -1