Question

(2x-3)²=(1-2x)² решите пж

Answer 1

${4x}^{2} - 12x + 9 = 1 - 4x + {4x}^{2} \\ - 12x + 9 = 1 - 4x \\ - 12x + 9 - 1 + 4x = 0 \\ - 8x + 8 = 0 \\ x - 1 = 0 \\ x = 1$

Answer 2

To solve the equation (2x - 3)² = (1 - 2x)², we'll first expand both sides of the equation and then proceed with the solution. The rule (a - b)² = a² - 2ab + b² will be used to expand the squared terms.

Expanding the left side:

(2x - 3)² = (2x - 3)(2x - 3) = 4x² - 6x - 6x + 9 = 4x² - 12x + 9

Expanding the right side:

(1 - 2x)² = (1 - 2x)(1 - 2x) = 1 - 2x - 2x + 4x² = 4x² - 4x + 1

Now, the equation becomes:

4x² - 12x + 9 = 4x² - 4x + 1

Subtract 4x² from both sides to eliminate the x² terms:

-12x + 9 = -4x + 1

Next, bring the x terms to one side of the equation by adding 12x and adding 1 to the other side:

-12x + 12x + 9 = -4x + 12x + 1 9 = 8x + 1

Now, isolate x by subtracting 1 from both sides:

9 - 1 = 8x 8 = 8x

Finally, divide both sides by 8 to solve for x:

x = 8/8 x = 1

So the solution to the equation is x = 1.