Question

（2х-3) ^2-(7-2х) ^2=2

Answer 1

Ответ:

x=5/2

Объяснение:

4x^2-12x+9-49+28x-4x^2=0

16x=40

×=5/2

Answer 2

To solve the equation $(2x - 3)^2 - (7 - 2x)^2 = 2$, you can use the difference of squares formula to simplify it:

$(2x - 3 + 7 - 2x)(2x - 3 - (7 - 2x)) = 2$

Now, simplify further:

$(2x + 4)(2x - 3 - 7 + 2x) = 2$

Combine like terms:

$(2x + 4)(4x - 10) = 2$

Now, distribute the terms on the left side:

$8x^2 - 20x + 16x - 40 = 2$

Combine like terms:

$8x^2 - 4x - 40 = 2$

Subtract 2 from both sides:

$8x^2 - 4x - 42 = 0$

Now, we have a quadratic equation in the form $ax^2 + bx + c = 0$, where $a = 8$, $b = -4$, and $c = -42$.

You can solve this quadratic equation using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Plug in the values:

$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(8)(-42)}}{2(8)}$

Now, calculate the values inside the square root:

$x = \frac{4 \pm \sqrt{16 + 1344}}{16}$

$x = \frac{4 \pm \sqrt{1360}}{16}$

$x = \frac{4 \pm 20\sqrt{17}}{16}$

Now, simplify:

$x = \frac{1}{4} \pm \frac{5\sqrt{17}}{4}$

So, the solutions to the equation are:

$x_1 = \frac{1}{4} + \frac{5\sqrt{17}}{4}$

$x_2 = \frac{1}{4} - \frac{5\sqrt{17}}{4}$