Question

(x-1)(x+1)(x-4)(x-2)=7​

Answer 1

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Answer 2

To solve the equation $(x-1)(x+1)(x-4)(x-2) = 7$, you can follow these steps:

1. Expand the left side of the equation:

$(x-1)(x+1)(x-4)(x-2) = 7$

$(x^2 - 1)(x^2 - 4x + 4) = 7$

2. Distribute the terms in the first parentheses to the terms in the second parentheses:

$x^2(x^2 - 4x + 4) - 1(x^2 - 4x + 4) = 7$

3. Simplify further:

$x^4 - 4x^3 + 4x^2 - x^2 + 4x - 4 = 7$

4. Combine like terms:

$x^4 - 4x^3 + 3x^2 + 4x - 4 = 7$

5. Move all terms to one side of the equation to set it equal to zero:

$x^4 - 4x^3 + 3x^2 + 4x - 4 - 7 = 0$

$x^4 - 4x^3 + 3x^2 + 4x - 11 = 0$

6. Now, you have a quartic equation. To solve this equation, you may need to use numerical methods or software to find its roots. Analytical solutions for quartic equations can be quite complex.

If you have access to a graphing calculator or mathematical software, you can graph the equation and find the values of $x$ where the graph intersects the x-axis, which would be the solutions to the equation. Alternatively, you can use numerical methods like the Newton-Raphson method or software such as MATLAB or Mathematica to find the roots of the equation.