Question

(x+1)•(x+2)-(x-3)•(x+4)=6

Answer 1

Ответ:

2

5±

13

Пошаговое объяснение:

(x

2

−5x+4)(x

2

−5x+6)=3

Сделаем замену. Пусть x^2-5x+4=tx

2

−5x+4=t , тогда получаем

\begin{gathered}t(t+2)=3\\ t^2+2t=3\\ t^2+2t+1=4\\ (t+1)^2=4\\ t+1=\pm2\\ t_1=1\\ t_2=-3\end{gathered}

t(t+2)=3

t

2

+2t=3

t

2

+2t+1=4

(t+1)

2

=4

t+1=±2

t

1

=1

t

2

=−3

Обратная замена

\begin{gathered}x^2-5x+4=1\\ x^2-5x+3=0\\D=b^2-4ac=(-5)^2-4\cdot 3=25-12=13\\ \\ x_{1,2}= \dfrac{5\pm \sqrt{13} }{2} \end{gathered}

x

2

−5x+4=1

x

2

−5x+3=0

D=b

2

−4ac=(−5)

2

−4⋅3=25−12=13

x

1,2

=

2

5±

13

\begin{gathered}x^2-5x+4=-3\\ x^2-5x+7=0\\ D=b^2-4ac=(-5)^2-4\cdot 1\cdot 7\ \textless \ 0\end{gathered}

x

2

−5x+4=−3

x

2

−5x+7=0

D=b

2

−4ac=(−5)

2

−4⋅1⋅7 \textless 0

Поскольку D<0, то квадратное уравнение действительных корней не имеет

Answer 2

To solve the equation (x+1)(x+2) - (x-3)(x+4) = 6, you can follow these steps:

1. First, expand both sets of parentheses:

   (x+1)(x+2) = x^2 + 3x + 2 (x-3)(x+4) = x^2 + x - 12

2. Now, substitute these expanded expressions back into the original equation:

   (x^2 + 3x + 2) - (x^2 + x - 12) = 6

3. Next, simplify the equation by combining like terms:

   x^2 + 3x + 2 - x^2 - x + 12 = 6

4. Continue simplifying:

   (x^2 - x^2) + (3x - x) + (2 + 12) = 6

5. Now, simplify further:

   2x + 14 = 6

6. Subtract 14 from both sides of the equation:

   2x + 14 - 14 = 6 - 14

   2x = -8

7. Finally, divide both sides by 2 to solve for x:

   (2x)/2 = (-8)/2

   x = -4

So, the solution to the equation (x+1)(x+2) - (x-3)(x+4) = 6 is x = -4.