biquadratic equations

A biquadratic equation is a 4-degree equation without the terms of degree 1 and 3.

To solve a biquadratic equation you have to do a change of variable: z = x2. Then you have to solve the quadratic equation and finally undo the change.

Example 1:

Example 2:
 
                      z = -1 →Φ
 
 
 
Exercise. Solve the following equations:
 
a) x4 - 25x2 + 144 = 0
 
b) x4 + 2x2 - 3 = 0
 
c) x6 + 9x3 + 8 = 0
 
 
 
 
 
Solutions: a) ±3, ±4; b) ±1; c) -2, -1

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