 |
Algebra problem (49) |  |
 |
Problem
For which values of x is true:
Solution
Square:
Extract factor (x-1):
so x4-4x2+x+2=(x-1)(x3+x2-3x-2)=0
This equation is true for x = -2 so a factor (x+2) may be extracted:
so x4-4x2+x+2=(x-1)(x+2)(x2-x-1)=0
Finally the ABC formula:
Note:
Condition is 2 - x2 > 0.
Solutions that do not satisfy thus criterium must be neglected.
These solutions are the result of squaring.
Solutions are:
