Question

(3x+4)^2 - (3x-1)(3x+1) = 41​

Answer 1

Ответ:

9x^2+24x+16-9x^2+1=41

24x=41-17

24x=24

x=1

Пошаговое объяснение:

Answer 2

To solve the given equation $(3x+4)^2 - (3x-1)(3x+1) = 41$, we'll follow these steps:

1. Expand the expressions on both sides of the equation.
2. Simplify the resulting expression.
3. Solve for $x$.

Let's go through these steps in detail:

1. Expand the expressions:

$$(3x+4)^2 = (3x+4)(3x+4) = 9x^2 + 24x + 16$$

Expanding the product of $(3x-1)(3x+1)$:

$$(3x-1)(3x+1) = 9x^2 - 1$$

2. Substitute the expanded expressions into the original equation:

$$9x^2 + 24x + 16 - (9x^2 - 1) = 41$$

3. Simplify the equation:

$$9x^2 + 24x + 16 - 9x^2 + 1 = 41$$

Simplifying further:

$$24x + 17 = 41$$

4. Isolate $x$ by subtracting 17 from both sides:

$$24x = 41 - 17$$

$$24x = 24$$

5. Finally, divide both sides by 24 to solve for $x$:

$$x = \frac{24}{24} = 1$$

So, $x = 1$ is the solution to the given equation $(3x+4)^2 - (3x-1)(3x+1) = 41$.