Question

(2x+1)^2+(x+3)*(x-3)=1​

Answer 1

Ответ:

Объяснение:

4x²+4x+1+x²-9-1=0

5x²+4x-9=0

D=16+180= 196

x1= (-4+14)/10= 1

x2= (-4-14)/10= -1,8

Answer 2

Ответ:

(2x+1)²+(x+3)(x-3)=1​

4x²+4x+1+x²-9-1=0

5x²+4x-9=0

D=4²-4*5*(-9)= 196

x1= (-4+14)/10= 1

x2= (-4-14)/10= -1,8

Ответ:-1,8; 1

Объяснение:

Ответы записываем сначала меньший корень потом больший

Answer 3

To solve the equation (2x+1)^2 + (x+3)*(x-3) = 1, follow these steps:

Step 1: Expand and simplify the left-hand side of the equation:

(2x + 1)^2 = (2x + 1) * (2x + 1) = 4x^2 + 4x + 1

(x + 3) * (x - 3) = x^2 - 9

So, the equation becomes:

4x^2 + 4x + 1 + x^2 - 9 = 1

Step 2: Combine like terms:

4x^2 + x^2 + 4x + 1 - 9 = 1

5x^2 + 4x - 8 = 1

Step 3: Move all terms to one side of the equation:

5x^2 + 4x - 9 = 0

Now we have a quadratic equation in the standard form (ax^2 + bx + c = 0) where a = 5, b = 4, and c = -9.

Step 4: Solve the quadratic equation using factoring, completing the square, or using the quadratic formula. In this case, we'll use the quadratic formula:

The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

For our equation, a = 5, b = 4, and c = -9, so the solutions for x are:

x = (-4 ± √(4^2 - 4 * 5 * -9)) / (2 * 5)

x = (-4 ± √(16 + 180)) / 10

x = (-4 ± √196) / 10

x = (-4 ± 14) / 10

Now, we have two possible solutions:

1. x = (10 - 4) / 10 x = 6 / 10 x = 0.6

2. x = (-4 - 14) / 10 x = -18 / 10 x = -1.8

So, the solutions to the equation are x = 0.6 and x = -1.8.