Question

(x - 1)(x² + x + 1) + x ² = x²(x + 1) - 2 x Рівняння

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the equation $(x - 1)(x^2 + x + 1) + x^2 = x^2(x + 1) - 2x$, we'll simplify both sides and then solve for $x$. Here are the steps:

1. Expand both sides of the equation:

   $(x - 1)(x^2 + x + 1) + x^2 = x^2(x + 1) - 2x$

   $x(x^2 + x + 1) - 1(x^2 + x + 1) + x^2 = x^3 + x^2 - 2x$

   $x^3 + x^2 + x - x^2 - x - 1 + x^2 = x^3 + x^2 - 2x$

2. Now, simplify the equation:

   $x^3 - x^2 - x - 1 + x^2 = x^3 + x^2 - 2x$

   $x^3 - x - 1 = x^3 + x^2 - 2x$

3. Subtract $x^3$ from both sides to cancel out the $x^3$ terms:

   $-x - 1 = x^2 - 2x$

4. Add $2x$ to both sides to isolate the $x^2$ term:

   $-x + 2x - 1 = x^2$

   $x - 1 = x^2$

5. Subtract $x$ from both sides to bring all terms to one side of the equation:

   $-1 = x^2 - x$

6. Rearrange the equation:

   $x^2 - x + 1 = 0$

Now, we have a quadratic equation $x^2 - x + 1 = 0$. You can use the quadratic formula to solve for (x:

The quadratic formula is $x = (-b ± √(b^2 - 4ac)) / (2a)$, where $a$, $b$, and $c$ are the coefficients from the quadratic equation $ax^2 + bx + c = 0$.

In this case, $a = 1$, $b = -1$, and $c = 1$. Plug these values into the quadratic formula:

$x = (-(-1) ± √((-1)^2 - 4(1)(1))) / (2(1))$

Now, simplify:

$x = (1 ± √(1 - 4))/2$

$x = (1 ± √(-3))/2$

Since the term inside the square root is negative ($√(-3)$), this equation has complex solutions. The solutions for $x$ are:

$x = (1 + √3i)/2$ and $x = (1 - √3i)/2$

So, the solutions are complex numbers.