Question

5x (x+3)^-5 (x+3) (x^-3x +9)-30 (x+2) (x-2)=75​

Answer 1

Пошаговое объяснение:

Что за галочки в примере? Это в квадрате?

Answer 2

Let's solve the equation step by step:

5x(x+3)^-5 * (x+3)(x^-3x+9) - 30(x+2)(x-2) = 75

First, simplify the equation:

5x(x+3)^-5 * (x+3)(x^-3x+9) - 30(x+2)(x-2) = 75

Now, let's deal with the factors and simplify further:

5x(x+3)^-5 * (x+3)(x^-3x+9) - 30(x+2)(x-2) = 75

5x(x+3)^-5 * (x^2 - 3x + 9) - 30(x^2 - 4) = 75

Now, distribute the factors:

5x(x^2 - 3x + 9)(x+3)^-5 - 30(x^2 - 4) = 75

Now, simplify further by expanding the expressions:

5x(x^2 - 3x + 9)(1/(x^5 + 15x^4 + 90x^3 + 270x^2 + 405x + 243)) - 30(x^2 - 4) = 75

Now, let's clear the denominators by multiplying both sides by the common denominator, which is the product of (x+3)^5 and (x^2 - 4):

5x(x^2 - 3x + 9) - 30(x^2 - 4)(x^5 + 15x^4 + 90x^3 + 270x^2 + 405x + 243) = 75(x+3)^5

Now, expand and simplify:

5x(x^2 - 3x + 9) - 30(x^7 + 15x^6 + 90x^5 + 270x^4 + 405x^3 + 243x^2 - 4x^2 + 60x - 360) = 75(x+3)^5

5x^3 - 15x^2 + 45x - 30x^7 - 450x^6 - 2700x^5 - 8100x^4 - 12150x^3 - 7290x^2 + 120x - 720 - 75(x+3)^5 = 0

Now, combine like terms and get all terms on one side of the equation:

-30x^7 - 450x^6 - 2700x^5 - 8100x^4 - 12150x^3 + 5x^3 - 7290x^2 - 15x^2 + 45x + 120x - 720 - 75(x+3)^5 = 0

-30x^7 - 450x^6 - 2700x^5 - 8100x^4 - 12150x^3 - 15x^3 - 7290x^2 - 15x^2 + 165x - 720 - 75(x+3)^5 = 0

Now, let's combine like terms and simplify further:

-30x^7 - 465x^6 - 2715x^5 - 8235x^4 - 12315x^3 - 7305x^2 + 165x - 720 - 75(x+3)^5 = 0

Now, this is a polynomial equation of the 7th degree. To solve it, you may need to use numerical methods or a graphing calculator, as finding exact solutions for high-degree polynomials can be quite complex.