Question

(х – 1)(х – 2)(х – 3)(х – 4) = 120

Answer 1

Ответ во вложениииииииии

Answer 2

To solve the equation $(x - 1)(x - 2)(x - 3)(x - 4) = 120$, we can follow these steps:

Step 1: Expand the left side of the equation: $(x - 1)(x - 2)(x - 3)(x - 4) = (x^2 - 3x + 2)(x^2 - 7x + 12)$

Step 2: Multiply the two quadratic expressions: $(x^2 - 3x + 2)(x^2 - 7x + 12) = x^4 - 7x^3 + 12x^2 - 3x^3 + 21x^2 - 36x + 2x^2 - 14x + 24$ $= x^4 - 10x^3 + 35x^2 - 50x + 24$

Step 3: Set the equation equal to 120: $x^4 - 10x^3 + 35x^2 - 50x + 24 = 120$

Step 4: Rearrange the equation to bring all terms to one side: $x^4 - 10x^3 + 35x^2 - 50x + 24 - 120 = 0$ $x^4 - 10x^3 + 35x^2 - 50x - 96 = 0$

Step 5: Solve the equation for x. This can be done either numerically or using symbolic methods like factoring or the rational root theorem. Since this is a quartic equation (4th degree), it might not have straightforward algebraic solutions.

Numerically, you can use numerical methods or a graphing calculator to find approximate solutions. If you're looking for exact solutions, you might need to use more advanced mathematical techniques or specialized software.

Please note that solving quartic equations can be quite complex and might involve advanced mathematical methods. If you're not comfortable with these methods, consulting a math expert or using appropriate software is recommended.