Answer :
The given equations do not have a simple, clear solution. They involve complex algebraic expressions that require further manipulation and analysis.
1. Equation 1: x^4 - 4x^3 - 13x + 4x = -12
Simplifying the equation, we have:
x^4 - 4x^3 - 9x = -12
There is no simple way to solve this equation. It is a quartic equation that may require advanced techniques such as factoring, using the rational root theorem, or employing numerical methods to find approximate solutions.
2. Equation 2: 4x^3 - 11x^2 + 7x + 10 = 0
This equation is a cubic equation, which can be solved using methods like factoring, synthetic division, or the cubic formula. However, the equation does not have simple integer solutions, so finding exact solutions may require numerical methods or approximations.
3. Equation 3: 4x^4 - 20x^3 = 60x^2 - 20x - 36
Rearranging the equation, we have:
4x^4 - 20x^3 - 60x^2 + 20x + 36 = 0
This quartic equation does not have a straightforward solution. Techniques like factoring, the rational root theorem, or numerical methods may be needed to find approximate solutions.
4. Equation 4: 3x^6 + 2x^4 + 10 = 4x^5 + 3x
To solve this equation, we need to rearrange it as follows:
3x^6 - 4x^5 + 2x^4 - 3x + 10 = 0
This equation is a sixth-degree polynomial, which is generally solved using numerical methods or approximation techniques. Finding exact solutions is usually challenging.
The given equations involve quartic and cubic equations, which often require advanced techniques or numerical methods to find solutions. The sixth-degree polynomial equation is also difficult to solve exactly.
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