Question

1) (x – 3) (x² + 3x +9)-(3x – 17) = x³-12;2) 5x – (4 - 2x + x²) (x+2)+ x (x - 1) (x + 1) = 0.​

Answer 1

Объяснение:

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Answer 2

Let's solve the given equations step by step:

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

First, expand the expressions:

$(x - 3)(x^2 + 3x + 9) = x(x^2 + 3x + 9) - 3(x^2 + 3x + 9)$ $= x^3 + 3x^2 + 9x - 3x^2 - 9x - 27$ $= x^3 - 27$

Now, rewrite the equation with the above expansion:

$x^3 - 27 - (3x - 17) = x^3 - 12$

Now, let's isolate the variable terms:

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

Combine like terms:

$x^3 - 3x - 10 = x^3 - 12$

Now, subtract $x^3$ from both sides:

$-3x - 10 = -12$

Add 12 to both sides:

$-3x - 10 + 12 = 0$

Simplify:

$-3x + 2 = 0$

Now, add 3x to both sides:

$-3x + 3x + 2 = 0 + 3x$

Simplify:

$2 = 3x$

Finally, divide by 3:

$\frac{2}{3} = x$

So, the solution to the first equation is $x = \frac{2}{3}$.

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

First, expand the expressions:

$(4 - 2x + x^2)(x + 2) = 4(x + 2) - 2x(x + 2) + x^2(x + 2)$

Now, distribute each term:

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

Simplify:

$8 + x^3 = 0$

Now, subtract 8 from both sides:

$x^3 = -8$

To find the solutions for this equation, take the cube root of both sides:

$x = \sqrt[3]{-8}$

Since the cube root of -8 is -2, the solution is:

$x = -2$

So, the solution to the second equation is $x = -2$.