Question

85.6. 1) 7x - (x - 2) = 13 – x(x – 6);3) -16 + (4 + x) = x²(x + 12);​

Answer 1

Ответ:

Объяснение:

1) 7x - (x - 2) = 13 – x(x – 6)

7x - x + 2 = 13 - x^2 + 6x

6x + 2 = 13 - x^2 + 6x

6x - 6x + x^2 = 13 - 2

x^2 = 11

x1 = $\sqrt{11}$

x2 = $-\sqrt{11}$

2)-16 + (4 + x) = x²(x + 12)

-16 + 4 + x = x^3 + 12x

x^3 + 12x - x -4 + 16 = 0

x^3 + 11x + 12 = 0

Дальше не умею

Answer 2

Let's solve these two equations step by step:

1. 7x - (x - 2) = 13 - x(x - 6)

First, simplify the equation by removing the parentheses:

7x - x + 2 = 13 - x(x - 6)

Combine like terms on both sides of the equation:

6x + 2 = 13 - x(x - 6)

Next, distribute the -x on the right side of the equation:

6x + 2 = 13 - (x^2 - 6x)

Now, distribute the negative sign inside the parentheses:

6x + 2 = 13 - x^2 + 6x

Rearrange the equation to isolate the quadratic term on one side:

x^2 + 6x - 6x - 2 - 13 = 0

Simplify further:

x^2 - 15 = 0

Now, we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = 0, and c = -15.

Use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 0, and c = -15:

x = (0 ± √(0² - 4(1)(-15))) / (2(1))

x = (0 ± √(60)) / 2

x = (0 ± √(4 * 15)) / 2

x = (0 ± 2√15) / 2

Now, simplify:

x = ±√15

So, the solutions to the equation are x = √15 and x = -√15.

2. -16 + (4 + x) = x²(x + 12)

First, simplify the equation:

-16 + 4 + x = x²(x + 12)

Combine like terms on the left side:

-12 + x = x²(x + 12)

Now, expand the right side of the equation:

-12 + x = x³ + 12x²

Rearrange the equation to isolate the cubic term on one side:

x³ + 12x² - x - 12 = 0

Now, this is a cubic equation. Unfortunately, there isn't a simple general formula for solving cubic equations like the quadratic formula. You can use numerical methods or a calculator to approximate the solutions. One possible approach is to use numerical approximation methods like the Newton-Raphson method or graph the equation to find approximate solutions.

So, for this equation, you would need to use numerical methods or a calculator to find the solutions.