Question

X(x²+2x+1)=2(x+1) решить уровнение​

Answer 1

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

x(x+1)^2=2(x+1)   :(x+1)

Answer 2

x(x²+2x+1)=2(x+1)

x(x+1)²=2(x+1)

x = -1

x(x+1)=2

x²+x-2=0

D = 1² - 4*1*(-2) = 9; √D = ±3

x1,2 = (-1 ±3) /2

x1 = -2; x2 =1

ответ x={-2;-1;1}

Answer 3

To solve the equation $X(x^2 + 2x + 1) = 2(x + 1)$, follow these steps:

Step 1: Expand the equation. Step 2: Move all terms to one side to set the equation equal to zero. Step 3: Factorize the equation, if possible. Step 4: Find the values of $x$ that satisfy the equation.

Let's go through each step:

Step 1: Expand the equation.

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

Step 2: Move all terms to one side to set the equation equal to zero.

$X(x^2 + 2x + 1) - 2(x + 1) = 0$

Step 3: Factorize the equation, if possible.

Now, let's factorize the left side of the equation:

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

Step 4: Find the values of $x$ that satisfy the equation.

The equation is now in factored form:

$X(x + 1)^2 - 2(x + 1) = 0$

To solve for $x$, we set each factor equal to zero and solve for $x$:

Setting $X(x + 1)^2 = 2(x + 1)$:

Case 1: $X = 0$ If $X = 0$, the equation becomes:

$0(x + 1)^2 - 2(x + 1) = 0$

Simplify:

$-2(x + 1) = 0$

Now, solve for $x$:

$x + 1 = 0$

$x = -1$

Case 2: $(x + 1)^2 = 2$ If $(x + 1)^2 = 2$, the equation becomes:

$X = \frac{2}{(x + 1)^2}$

There is no specific value of $x$ for this case since $X$ is defined in terms of $x$.

So, the solution to the equation is $x = -1$ and $X = \frac{2}{(x + 1)^2}$.