Question

1)(x-3)(x^2+3x+9)-(3x-17)=x^3-12 2)5x-(4-2x+x^2) (x+2)+x(x-1)(x+1)=0

Answer 1

Ответ:

1)

(x-3)(x²+3x+9)-(3x-17)=x³-12

x³-27-3x+17=x³-12

x³-10-3x=x³-12

x³-3x-x³=10-12

-3x=-2

x=2/3

2)

5x-(4-2x+x²)(x+2)+x(x-1)(x+1)=0

5x-(8+x³)+x(x²-1)=0

5x-8-x³+x³-x=0

4x=8

x=2

Answer 2

Let's solve each equation step by step:

1. (x - 3)(x^2 + 3x + 9) - (3x - 17) = x^3 - 12

Expanding the left side of the equation:

x(x^2 + 3x + 9) - 3(x^2 + 3x + 9) - (3x - 17) = x^3 - 12

x^3 + 3x^2 + 9x - 3x^2 - 9x - 27 - 3x + 17 = x^3 - 12

Combining like terms:

x^3 + 3x^2 - 3x^2 + 9x - 9x - 3x + 17 - 27 = x^3 - 12

Simplifying:

x^3 + 3x - 3x - 3x + 17 - 27 = x^3 - 12

x^3 - 9x + 17 - 27 = x^3 - 12

x^3 - 9x - 10 = x^3 - 12

Subtracting x^3 from both sides:

-9x - 10 = -12

Adding 10 to both sides:

-9x = -2

Dividing by -9:

x = 2/9

Therefore, the solution to the equation is x = 2/9.

2. 5x - (4 - 2x + x^2)(x + 2) + x(x - 1)(x + 1) = 0

Expanding the terms:

5x - (4x + 8 - 2x^2 - 4x + x^3) + x(x^2 - 1) = 0

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

Combining like terms:

5x - 4x + 4x + 2x^2 + x^2 - x - 8 = 0

3x + 3x^2 - x - 8 = 0

Rearranging the terms:

3x^2 + 3x - x - 8 = 0

3x^2 + 2x - 8 = 0

Unfortunately, this equation cannot be easily factored or solved using simple algebraic techniques. You would need to use numerical methods, such as graphing, factoring using the quadratic formula, or approximation methods, to find the solution(s) for x.

If you need an approximate solution, you can use numerical methods or a calculator to find the roots.