Question

Розв'яжіть рівняння: (3x-1)(x+4)=(2x+3)(x+3)-17. Решение через дискриминант Пожалуйста срочно помогите ​

Answer 1

Ответ:

$Net..resheniy$

Объяснение:

$(3x-1)(x+4)=(2x+3)(x+3)-17\\ 3x^{2} +11x-4=2x^{2} +9x-8\\ x^{2} +2x+4=0\\ D=4-4*1*4 < 0\\ Net..resheniy$

Answer 2

Solving the Equation Using the Discriminant

To solve the equation *(3x-1)(x+4) = (2x+3)(x+3) - 17* using the discriminant, we first need to expand and simplify the equation and then apply the quadratic formula to find the solutions.

Step 1: Expand and Simplify the Equation

Expanding the equation gives us: *(3x-1)(x+4) = (2x+3)(x+3) - 17* Expanding further: *3x^2 + 12x - x - 4 = 2x^2 + 3x + 6x + 9 - 17* Simplifying: *3x^2 + 11x - 4 = 2x^2 + 9x - 8*

Step 2: Rearrange the Equation

Rearranging the equation to set it equal to zero: *3x^2 - 2x^2 + 11x - 9x - 4 + 8 = 0* * x^2 + 2x - 4 = 0*

Step 3: Identify the Coefficients

From the equation *x^2 + 2x - 4 = 0*, we can identify the coefficients: - a = 1 - b = 2 - c = -4

Step 4: Calculate the Discriminant

The discriminant, denoted by Δ, is calculated using the formula: *Δ = b^2 - 4ac*

Substitute the values of a, b, and c into the formula: *Δ = 2^2 - 4(1)(-4)* *Δ = 4 + 16* *Δ = 20*

Step 5: Use the Quadratic Formula to Find the Solutions

The solutions to the quadratic equation *ax^2 + bx + c = 0* are given by the quadratic formula: *x = (-b ± √Δ) / (2a)*

Substitute the values of a, b, and Δ into the quadratic formula: *x = (-2 ± √20) / (2*1)* *x = (-2 ± 2√5) / 2* *x = -1 ± √5*

Therefore, the solutions to the equation are: x = -1 + √5 and x = -1 - √5.