Answer:
The given equation is:
x^3 - 4x = 2
To find the solutions, we can start by rearranging the equation to get all the terms on one side:
x^3 - 4x - 2 = 0
Next, we can use either factoring or numerical methods to find the solutions. One possible method is to use synthetic division with the known solutions (or roots) to factor the polynomial. From the given solutions, we can see that x ≈ -2.0, x ≈ -0.2, and x ≈ 9.8 are all possible roots. Trying these values in synthetic division, we get:
For x ≈ -2.0:
-2.0 | 1 0 -4 -2
| -2 4 -0.8
---------------
1 -2 0 -2.8
The remainder is not zero, so x ≈ -2.0 is not a solution.
For x ≈ -0.2:
-0.2 | 1 0 -4 -2
| -0.2 0.72 0.456
-----------------
1 -0.2 -3.28 -1.544
The remainder is not zero, so x ≈ -0.2 is not a solution.
For x ≈ 9.8:
9.8 | 1 0 -4 -2
| 9.8 73.528 721.6832
---------------------
1 9.8 69.528 719.6832
The remainder is not zero, so x ≈ 9.8 is also not a solution.
Therefore, there are no valid solutions to the given equation among the provided options.
Explanation:
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