Question

Уравнение 12-(4-x)^2=x (3-x)​

Answer 1

$12 - (4-x)^{2} =x(3-x)$

Формула сокращенного умножения, раскрыть скобки, перенести все в одну часть

$12-(16-8x+x^{2}) = 3x-x^{2}\\12-16+8x-x^{2} -3x+x^{2} =0\\-4+5x=0\\5x=4\\x= \frac{4}{5} \\x=0,8$

Проверка:

$12-(4-0,8)^{2} =0,8(3-0,8)\\12-3,2^2=0,8 * 2,2\\1,76 = 1,76$

Answer 2

To solve the equation 12 - (4-x)^2 = x(3-x), follow these steps:

Step 1: Expand the squared term on the left side of the equation. Step 2: Simplify the equation by combining like terms. Step 3: Move all terms to one side of the equation to set it to zero. Step 4: Factorize the quadratic equation. Step 5: Solve for the values of x.

Let's go through each step in detail:

Step 1: Expand (4-x)^2 = (4-x)(4-x) = 16 - 4x - 4x + x^2 = 16 - 8x + x^2.

Step 2: Substitute the expanded term back into the original equation: 12 - (16 - 8x + x^2) = x(3 - x).

Step 3: Combine like terms on the left side: 12 - 16 + 8x - x^2 = x(3 - x).

Now, the equation becomes: -4 + 8x - x^2 = 3x - x^2.

Step 4: Move all terms to one side of the equation: -4 + 8x - x^2 - 3x + x^2 = 0.

Simplify further: 5x - 4 = 0.

Step 5: To solve for x, add 4 to both sides: 5x = 4.

Finally, divide both sides by 5 to get the value of x: x = 4/5.

So, the solution to the equation is x = 4/5.