Question

Решите уравнение (4x-3)^2-(2x+1)^2=0

Answer 1

(4x-3)^2-(2x+1)^2=0
Приравниваем к нулю.
4х-3=0
4х=3
х=3/4
2х+1=0
2х=-1
х=-1/2
Ответ: 3/4; -1/2

Answer 2

To solve the equation $(4x-3)^2 - (2x+1)^2 = 0$, we'll first factor it using the difference of squares formula, and then solve for $x$.

The difference of squares formula states that $a^2 - b^2 = (a + b)(a - b)$.

In our equation, $a = (4x - 3)$ and $b = (2x + 1)$. Therefore, the equation becomes:

$(4x - 3 + 2x + 1)(4x - 3 - 2x - 1) = 0$.

Now, let's simplify this:

$(6x - 2)(2x - 4) = 0$.

Now, the equation is in factored form. To find the values of $x$, set each factor to zero and solve for $x$:

1. $6x - 2 = 0$ Add 2 to both sides: $6x = 2$ Divide by 6: $x = \frac{2}{6} = \frac{1}{3}$.

2. $2x - 4 = 0$ Add 4 to both sides: $2x = 4$ Divide by 2: $x = \frac{4}{2} = 2$.

So, the solutions to the equation are $x = \frac{1}{3}$ and $x = 2$.