Question

(2x^2+3x)^2-7(2x^2+3x)=-10

Answer 1

Пусть 2x²+3x=t, тогда:

t²-7t+10=0

D= 49-40= 9

t1= (7+3)/2= 5

t2= (7-3)/2= 2

1) 2x²+3x=5

2x²+3x-5=0

D=9+40= 49

x1= (-3+7)/4= 1

x2= (-3-7)/4= -2,5

2) 2x²+3x=2

2x²+3x-2=0

D=9+16= 25

x3= (-3+5)/4= 0,5

x4= (-3-5)/4= -2

Ответ: x1= 1, x2= -2,5, x3= 0,5,  x4= -2

Answer 2

вот решение, ответов получилось много :)

Answer 3

To solve the given equation (2x^2 + 3x)^2 - 7(2x^2 + 3x) = -10, we can follow these steps:

Step 1: Expand the left side of the equation using the distributive property. Step 2: Simplify the equation. Step 3: Solve for x.

Let's proceed with the steps:

Step 1: Expand the left side of the equation: (2x^2 + 3x)^2 - 7(2x^2 + 3x) = (2x^2 + 3x)(2x^2 + 3x) - 7(2x^2 + 3x)

Using the distributive property: = (4x^4 + 6x^3 + 6x^3 + 9x^2) - (14x^2 + 21x)

Step 2: Simplify the equation: Combine like terms: = 4x^4 + 12x^3 + 9x^2 - 14x^2 - 21x

Now the equation becomes: = 4x^4 + 12x^3 - 5x^2 - 21x

Step 3: Set the equation to -10 and solve for x: 4x^4 + 12x^3 - 5x^2 - 21x = -10

Move all terms to one side of the equation: 4x^4 + 12x^3 - 5x^2 - 21x + 10 = 0

This is a fourth-degree polynomial equation, which can be challenging to solve algebraically. Unfortunately, I am unable to find the exact solutions for this equation. You can solve it using numerical methods or graphing techniques to approximate the solutions. Alternatively, you can use computational tools like Wolfram Alpha or software like Python with libraries like NumPy to find numerical solutions.