Question

( 2-3х)^2=(2-х)(2+х)

Answer 1

${(2 - 3x)}^{2} = (2 - x)(2 + x) \\ 4 - 12x + 9 {x}^{2} = 4 - {x}^{2} \\ 9 {x}^{2} + {x}^{2} - 12x + 4 - 4 = 0 \\ 10 {x}^{2} - 12x = 0 \\ 2x(5x - 6) = 0 \\ \\ 2x = 0 \\ x_1 = 0 \\ \\ 5x - 6 = 0 \\ 5x = 6 \\ x = \frac{6}{5} \\ x_2 = 1.2$

Answer 2

Ответ:

Пошаговое объяснение:

( 2-3х)^2=(2-х)(2+х)

4 - 12x + 9x² = 4 - x²

9x² + x² - 12x + 4 - 4= 0

10x²- 12x = 0

2x*(5x - 6) = 0

2x = 0    или  5x - 6 = 0

x = 0               5x = 6

                        x = 6:5

                        x = 1,2

ответ: x₁ = 0 ;       x₂ = 1,2

Answer 3

To solve the equation (2-3x)^2 = (2-x)(2+x), let's expand both sides and simplify:

Expanding the left side: (2-3x)^2 = (2-3x)(2-3x) = 4 - 6x - 6x + 9x^2 = 4 - 12x + 9x^2.

Expanding the right side: (2-x)(2+x) = 4 - x^2.

Setting the two sides equal to each other, we have:

4 - 12x + 9x^2 = 4 - x^2.

Now, let's simplify and rearrange the equation:

9x^2 + x^2 - 12x = 0.

Combining like terms:

10x^2 - 12x = 0.

Factor out x:

x(10x - 12) = 0.

Now we have two possibilities:

1. x = 0
2. 10x - 12 = 0

For the second equation, solving for x:

10x - 12 = 0 10x = 12 x = 12/10 x = 6/5

Therefore, the solutions to the equation (2-3x)^2 = (2-x)(2+x) are x = 0 and x = 6/5.