Solve the following equation

Question

solve the equation x^6-2x^3-3=0

Answer 1

This is a "quadratic in disguise"  

 

Let y = x^3.  Then y^2 = x^6 and the equation is  

 

y^2 - 2y - 3 = 0

(y - 3)(y + 1) = 0

y = 3  or  y = -1  

 

Remember y = x^3 so  

 

x^3 = 3  or  x^3 = -1  

x = ³√3  or  x = -1  

 

Check:  (³√3)^6 - 2(³√3)^3 - 3 = 9 - 6 - 3 = 0  

            (-1)^6 - 2(-1)^3 - 3 = 1 + 2 - 3 = 0