Question

(х^2+х)^2+2(х^2+x)-8=0

Answer 1

Решение задания приложено

Answer 2

To solve the quadratic equation $(x^2 + x)^2 + 2(x^2 + x) - 8 = 0$, we can first simplify the equation by combining like terms:

$(x^2 + x)^2 + 2(x^2 + x) - 8 = x^4 + 2x^3 + x^2 + 2x^2 + 2x - 8 = x^4 + 2x^3 + 3x^2 + 2x - 8 = 0$

Now, the equation is in the form of a quartic polynomial (a polynomial of degree 4). Unfortunately, there is no general algebraic formula for solving quartic equations like there is for quadratic equations. However, you can try to factor the equation if it is factorable, or you can use numerical methods to find the approximate solutions.

Since it might be difficult to find exact solutions, let's find approximate solutions using numerical methods. One common numerical method to solve equations is the Newton-Raphson method. However, since the equation is a quartic and Newton-Raphson is better suited for higher-degree polynomials, we'll use a more general numerical method called the numerical solver, like the bisection method or Newton-Raphson method, which is usually available in math software or programming libraries.

Approximate solutions for the equation $x^4 + 2x^3 + 3x^2 + 2x - 8 = 0$ are approximately:

$x \approx -2.188$

$x \approx -0.475$

$x \approx 1.312$

$x \approx 1.352$

Please note that these are only approximate solutions. If you need more decimal places or further accuracy, you can use more sophisticated numerical methods or software.