Question

(3а + 4)^2 - (3а-1) (1+3а)=49

Answer 1

Ответ:

$a=\frac{4}{3}$

Объяснение:

$(3a+4)^2-(3a-1)(1+3a)=49\\(9a^2+24a+16)-(9a^2-1)=49\\9a^2+24a+16-9a^2+1=49\\24a+17=49\\24a=32\\a=\frac{32}{24}=\frac{4}{3}$

Answer 2

Ответ:

............................

Answer 3

Let's solve the given quadratic equation for the variable "а". The equation is:

(3а + 4)^2 - (3а - 1)(1 + 3а) = 49

First, let's expand the squared term and the product term:

(9а^2 + 24а + 16) - (3а^2 - 3а + 3а - 1) = 49

Simplify each term:

9а^2 + 24а + 16 - 3а^2 + 3а - 3а + 1 = 49

Now combine like terms:

(9а^2 - 3а^2) + (24а + 3а - 3а) + (16 + 1) = 49

Simplify further:

6а^2 + 24а + 17 = 49

Now, subtract 49 from both sides to set the equation to zero:

6а^2 + 24а + 17 - 49 = 0

Combine constants:

6а^2 + 24а - 32 = 0

Divide the entire equation by 2 to simplify:

3а^2 + 12а - 16 = 0

Now, we have a quadratic equation in standard form. To solve this quadratic equation, we can use the quadratic formula:

For a quadratic equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, the coefficients are: a = 3 b = 12 c = -16

Plugging these values into the formula:

а = (-12 ± √(12^2 - 4 * 3 * -16)) / (2 * 3) а = (-12 ± √(144 + 192)) / 6 а = (-12 ± √336) / 6 а = (-12 ± √(4 * 84)) / 6 а = (-12 ± 2√84) / 6 а = -2 ± √84 / 3

So, the solutions for "а" are:

а = (-2 + √84) / 3 а = (-2 - √84) / 3

You can further simplify the square root if needed.