Question

Решить (х+2)^4+2х^2+8х-16=0

Answer 1

(x+2)^4+2(x²+4x+4)-24=0
(x+2)^4+2(x+2)²-24=0
(x+2)²=a
a²+2a-24=0
a1+a2=-2 U a1*a2=-24
a1=-6⇒(a+2)²=-6 нет решения
a2=4⇒(x+2)²=4
x+2=-2 или х+2=2
х=-4 или х=0
Ответ х=-4 или х=0

Answer 2

\\\\\\\\\\\\\\\\\\\\\\\\\\\

Answer 3

I can help you solve this equation. The equation is $(x+2)^4+2x^2+8x-16=0$. To solve it, we need to expand the fourth power of $(x+2)$ and then collect the like terms. We get:

$$x^4+8x^3+24x^2+32x+16+2x^2+8x-16=0$$ $$x^4+8x^3+26x^2+40x=0$$

Next, we can factor out $x$ from each term and get:

$$x(x^3+8x^2+26x+40)=0$$

Now, we can use the zero product property and set each factor equal to zero. We get:

$$x=0$$ $$x^3+8x^2+26x+40=0$$

The first equation gives us one solution: $x=0$. The second equation is a cubic equation, which is harder to solve by hand. We can use an online calculator to find the approximate solutions. One such calculator is [Mathway](https://www.mathway.com/ru/Algebra), which gives us the following solutions:

$$x\approx -6.449$$ $$x\approx -0.7755+1.343i$$ $$x\approx -0.7755-1.343i$$

These are the four solutions of the original equation. You can check them by plugging them back into the equation and verifying that they make it equal to zero. I hope this helps.