Question

(4x-3)(4x+3)-(4x-1)^2=3х решите уравнение

Answer 1

$(4x - 3)(4x + 3) - {(4x - 1)}^{2} = 3x \\ 16 {x}^{2} - 9 - 16 {x}^{2} + 8x - 1 - 3x = 0 \\ 5x - 10 = 0 \\ 5x = 10 \\ x = 2$

Вот)

Answer 2

To solve the equation, we'll first simplify the expression on the left-hand side and then equate it to 3x.

Given expression: (4x-3)(4x+3) - (4x-1)^2 = 3x

Step 1: Simplify the expression on the left-hand side. Expand (4x-3)(4x+3): (4x-3)(4x+3) = 16x^2 - 12x + 12x - 9 = 16x^2 - 9

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

Substitute the simplified expressions back into the equation: (16x^2 - 9) - (16x^2 - 8x + 1) = 3x

Step 2: Combine like terms: 16x^2 - 9 - 16x^2 + 8x - 1 = 3x

Step 3: Simplify further: 8x - 10 = 3x

Step 4: Isolate the variable x on one side of the equation: 8x - 3x = 10 5x = 10

Step 5: Solve for x: x = 10/5 x = 2

So the solution to the equation is x = 2.