x^{6}  9x^{3} + 8 = 0
Solution
x^{6}  9x^{3} + 8 = 0
Let x^{3} = t and Put in the given equation
t^{2}  9t + 8 = 0
Comparing the given equation with at^{2} + bt + c = 0, we get
a = 1,
b = 9,
c = 8
By Quardratic formula, we have
Putting the values of a, b, and c in the formula
Either 

OR 









By letting x^{3} = t, Putting the value of t, we get 

x^{3} = 
1  (i) 


x^{3} = 
8  (ii) 

By equation (i) x^{3} = 1
x^{3}  1 = 0
x^{3}  1^{3} = 0
(x  1)(x^{2} + x + 1) = 0
Either 
x  1 = 0 
OR 
x^{2} + x + 1 = 0 

x = 1 

By Quadratic formula









By equation (ii) x^{3} = 8
x^{3}  8 = 0
x^{3}  (2)^{3} = 0
(x  2)(x^{2} + 2x + 4) = 0
Either 
x  2 = 0 
OR 
x^{2} + 2x + 4 = 0 

x = 2 

By Quadratic formula

























From equation (i) and (ii), we get
Hence the Solution Set of given equation is