Question

(x²-4x)²-4(x²+4x)-5=0​

Answer 1

Ответ:

$x { }^{4} - 2x {}^{2} + 16x {}^{2} - 4x {}^{2} - 16x - 5$

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Answer 2

To solve the quadratic equation $(x^2 - 4x)^2 - 4(x^2 + 4x) - 5 = 0$, we can start by simplifying it:

$$(x^2 - 4x)^2 - 4(x^2 + 4x) - 5 = 0$$

Let's break it down step by step:

1. Expand $(x^2 - 4x)^2$: $(x^2 - 4x)^2 = x^4 - 8x^3 + 16x^2$

2. Expand $-4(x^2 + 4x)$: $-4(x^2 + 4x) = -4x^2 - 16x$

Now, the equation becomes:

$$x^4 - 8x^3 + 16x^2 - 4x^2 - 16x - 5 = 0$$

Combine like terms:

$$x^4 - 8x^3 + 12x^2 - 16x - 5 = 0$$

Now, this is a quartic equation. Unfortunately, quartic equations do not have a general algebraic solution like quadratic equations (which can be solved using the quadratic formula). You will typically need to use numerical methods or specialized software to find approximate solutions for quartic equations.

If you want to find numerical approximations for the roots of this equation, you can use numerical methods like Newton's method or use software like Python with libraries like NumPy or SymPy to find the roots.