Question

12 - (4 - x)² = (x + 1) (1 - x) - 3x.​

Answer 1

Ответ:

Пошаговое объяснение:

12-(16-8х-х²)=х+1+1-х²-3х

12-16+8х+х²=2-х²-2х

10х=2+16-12

10х=6

х=0,6

Answer 2

Ответ:

Пошаговое объяснение:

Answer 3

To solve the equation $12 - (4 - x)^2 = (x + 1)(1 - x) - 3x$, we'll follow these steps:

Step 1: Expand the squared term and the product on the right side of the equation. Step 2: Simplify both sides of the equation. Step 3: Solve for $x$.

Let's proceed with solving the equation:

Step 1: Expand the squared term and the product on the right side of the equation: $12 - (4 - x)^2 = (x + 1)(1 - x) - 3x$

Expanding the squared term: $12 - (16 - 8x + x^2) = (x + 1)(1 - x) - 3x$ $12 - 16 + 8x - x^2 = x - x^2 + 1 - x - 3x$

Step 2: Simplify both sides of the equation: $-4 + 8x - x^2 = 1 - 3x$

Step 3: Solve for $x$: Combine like terms on both sides: $x^2 + 11x - 5 = 0$

Now, we have a quadratic equation in standard form. To solve for $x$, you can either factor it, use the quadratic formula, or complete the square. In this case, the quadratic equation doesn't seem to factor easily, so let's use the quadratic formula:

The quadratic formula states that for an equation of the form $ax^2 + bx + c = 0$, the solutions for $x$ are given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For our equation $x^2 + 11x - 5 = 0$, $a = 1$, $b = 11$, and $c = -5$.

Calculating the discriminant ($b^2 - 4ac$): $b^2 - 4ac = 11^2 - 4(1)(-5) = 121 + 20 = 141$

Since the discriminant is positive, we have two distinct real solutions: $x = \frac{-11 \pm \sqrt{141}}{2}$

So the solutions for $x$ are: $x = \frac{-11 + \sqrt{141}}{2} \quad \text{and} \quad x = \frac{-11 - \sqrt{141}}{2}$

These are the approximate decimal values of the solutions. If you need more precise values, you can use a calculator to evaluate the square root and perform the arithmetic.