Question

(x-5)(x-4)(x-3)(x-2)=24​

Answer 1

Пошаговое объяснение:

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Answer 2

To solve the equation $(x-5)(x-4)(x-3)(x-2) = 24$, you can follow these steps:

1. Expand the left side of the equation: $(x-5)(x-4)(x-3)(x-2) = (x^2 - 9x + 20)(x^2 - 5x + 6)$

2. Expand the quadratic expressions further: $(x^2 - 9x + 20)(x^2 - 5x + 6) = x^4 - 5x^3 + 6x^2 - 9x^3 + 45x^2 - 54x + 20x^2 - 100x + 120$ $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = x^4 - 14x^3 + 71x^2 - 154x + 120$

3. Now you have the equation: $x^4 - 14x^3 + 71x^2 - 154x + 120 = 24$

4. Move all terms to one side to set the equation to zero: $x^4 - 14x^3 + 71x^2 - 154x + 96 = 0$

5. At this point, you can try to factor the equation. Unfortunately, the equation does not seem to factor easily into simple linear or quadratic factors.

6. You might need to resort to numerical methods or approximations to find the solutions. One common approach is to use numerical methods such as the Newton-Raphson method or graphing techniques to find the approximate values of $x$ that satisfy the equation.

Keep in mind that polynomial equations of degree 4 or higher can be quite challenging to solve algebraically in general cases. Numerical methods can provide approximate solutions when algebraic methods are not feasible.