Question

Решите уравнение : (x+3)2-x= (x-2)(2+x) решите пж,скоро экзамены вот ищу примеры для подготовки,не знаю как делать ибо не проходили вбще хелп

Answer 1

(x+3)²-x=(x-2)(2+x)
x²+5x+9=(x-2)(x+2)
x²+5x+9=x²-4
5x+13=0
5x=-13
ответ: x=-13/5=-2 3/5 = -2,6

Answer 2

Solving the Equation: (x+3)^2 - x = (x-2)(2+x)

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

Step 1: Expand the equation Step 2: Simplify and combine like terms Step 3: Solve for x

Let's go through each step in detail:

Step 1: Expand the equation Expand the equation by squaring the binomial (x+3) and multiplying the binomials (x-2) and (2+x):

(x+3)^2 - x = (x-2)(2+x) (x+3)(x+3) - x = (x-2)(2+x) (x^2 + 6x + 9) - x = (x-2)(2+x)

Step 2: Simplify and combine like terms Simplify and combine like terms on both sides of the equation:

x^2 + 6x + 9 - x = 2x^2 - 4 x^2 + 5x + 9 = 2x^2 - 4

Step 3: Solve for x To solve for x, we need to move all the terms to one side of the equation and set it equal to zero:

2x^2 - x^2 + 5x + 4 - 9 = 0 x^2 + 5x - 5 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 5, and c = -5. Substituting these values into the quadratic formula:

x = (-5 ± √(5^2 - 4(1)(-5))) / (2(1)) x = (-5 ± √(25 + 20)) / 2 x = (-5 ± √45) / 2

Simplifying further:

x = (-5 ± √(9 * 5)) / 2 x = (-5 ± 3√5) / 2

Therefore, the solutions to the equation (x+3)^2 - x = (x-2)(2+x) are:

x = (-5 + 3√5) / 2 x = (-5 - 3√5) / 2

Please note that these solutions are approximate values and can be further simplified if needed.

I hope this helps! Let me know if you have any further questions.