Question

(х^{2}+3х-25)^{2}-2(х^{2}+3х-25)=-7  

Answer 1

(х^{2}+3х-25)^{2}-2(х^{2}+3х-25)=-7

(x2+3x-25)^2-2(x^2+3x-25)=(x^2+3x-27)(x^2+3x-25)

(x^2+3x-27)(x^2+3x-25)=-7

После разложения каждой части по отдельности(по Дискрименанту) мы видим, что действительных решений нет.

Ответ: нет действительных решений

Answer 2

To solve the equation (x^2 + 3x - 25)^2 - 2(x^2 + 3x - 25) = -7, we can start by simplifying it step by step:

Let's substitute y = (x^2 + 3x - 25) to simplify the equation:

y^2 - 2y = -7

Rearranging the equation, we have:

y^2 - 2y + 7 = 0

Now, we can solve this quadratic equation for y. However, it is important to note that the original equation will have multiple solutions for x, but we will find the solutions for y first:

Using the quadratic formula, where a = 1, b = -2, and c = 7:

y = (-(-2) ± √((-2)^2 - 4(1)(7))) / (2(1)) y = (2 ± √(4 - 28)) / 2 y = (2 ± √(-24)) / 2 y = (2 ± 2√6i) / 2

Simplifying further:

y = 1 ± √6i

Now, we can substitute back y = (x^2 + 3x - 25):

x^2 + 3x - 25 = 1 ± √6i

To find the solutions for x, we can solve two separate equations:

1. x^2 + 3x - 25 = 1 + √6i
2. x^2 + 3x - 25 = 1 - √6i

Let's solve each equation separately:

1. x^2 + 3x - 25 = 1 + √6i

Rearranging the equation, we have:

x^2 + 3x - 26 = √6i

To solve this equation, we'll square both sides:

(x^2 + 3x - 26)^2 = (√6i)^2 (x^2 + 3x - 26)^2 = -6

Expanding the left side of the equation:

x^4 + 6x^3 - 5x^2 - 102x + 676 = -6

Rearranging and simplifying:

x^4 + 6x^3 - 5x^2 - 102x + 682 = 0

This is a quartic equation, and finding its solutions can be a complex process. There isn't a simple algebraic solution for quartic equations in general. You may need to use numerical methods or software to approximate the solutions.

Similarly, we can solve the second equation:

2. x^2 + 3x - 25 = 1 - √6i

Rearranging the equation, we have:

x^2 + 3x - 26 = -√6i

To solve this equation, we'll square both sides:

(x^2 + 3x - 26)^2 = (-√6i)^2 (x^2 + 3x - 26)^2 = -6

Expanding the left side of the equation:

x^4 + 6x^3 - 5x^2 - 102x + 676 = -6

Rearranging and simplifying:

x^4 + 6x^3 - 5x^2 - 102x + 682 = 0

This equation is identical to the one we obtained in equation 1). Hence, the solutions for both equations will be the same.

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