Question

X1+x2=-40 x1×x2=-1600

Answer 1

Ответ:

Объяснение:

$\[\left\{\begin{gathered}{x_1}+{x_2}=-40\hfill\\{x_1}\cdot{x_2}=-1600\hfill\\\end{gathered}\right.\Leftrightarrow\left\{\begin{gathered}{x_1}=-40-{x_2}\hfill\\{x_1}\cdot{x_2}=-1600\hfill\\\end{gathered}\right.\Leftrightarrow\]$

$\[\left\{\begin{gathered}{x_1}=-40-{x_2}\hfill\\(-40-{x_2})\cdot{x_2}=-1600\hfill\\\end{gathered}\right.\Leftrightarrow\left\{\begin{gathered}{x_1}=-40-{x_2}\hfill\\-40{x_2}-x_2^2+1600=0\hfill\\\end{gathered}\right.\]$

Решим квадратное уравнение:

$\[\begin{gathered}-40{x_2}-x_2^2+1600=0\hfill\\-40x-{x^2}+1600=0\;\;\;\;|\cdot (-1)\hfill\\{x^2}+40x-1600=0\hfill\\D={b^2}-4ac={40^2}+4\cdot 1\cdot1600=1600+6400=8000\hfill\\\end{gathered}\]$

$\[\begin{gathered}{x_{1;2}}=\frac{{-b\pm\sqrt D}}{{2a}}=\frac{{-40\pm\sqrt {8000}}}{{2\cdot 1}}=\frac{{-40\pm40\sqrt 5}}{2}\hfill\\{x_1}=\frac{{-40+40\sqrt 5}}{2}=\frac{{2(-20+20\sqrt 5)}}{2}=-20+20\sqrt 5\hfill\\{x_2}=\frac{{-40-40\sqrt 5}}{2}=\frac{{2(-20-20\sqrt 5)}}{2}=-20-20\sqrt 5\hfill\\\end{gathered}\]$

Итак, мы нашли x₂.

${x_2}=-20+20\sqrt 5$

или

${x_2}=-20-20\sqrt 5$

Найдем x₁

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$\[\begin{gathered}{x_1}=-40-(-20+20\sqrt 5)=-20-20\sqrt 5\hfill\\\end{gathered}\]$

При ${x_2}=-20-20\sqrt 5$

$\[{x_1}=-40-(-20-20\sqrt 5)=-20+20\sqrt 5\]$

Ответ: $\[{x_1}=-20-20\sqrt 5;\;\;\;{x_2}=-20+20\sqrt 5\]$   или $\[{x_1}=-20+20\sqrt 5;{x_2}=-20-20\sqrt 5\]$

Answer 2

To find the values of x1 and x2, we can use the given equations:

1. x1 + x2 = -40
2. x1 * x2 = -1600

We can use substitution or elimination method to solve this system of equations. Let's use the substitution method:

Step 1: Solve one equation for one variable in terms of the other variable. From equation (1), we can write: x1 = -40 - x2

Step 2: Substitute the expression for x1 from Step 1 into equation (2): (-40 - x2) * x2 = -1600

Step 3: Expand and simplify the equation: -40x2 - x2^2 = -1600

Step 4: Move all terms to one side to set the equation to zero: x2^2 + 40x2 - 1600 = 0

Step 5: Factorize or use the quadratic formula to solve for x2: (x2 + 60)(x2 - 20) = 0

Setting each factor to zero and solving for x2:

1. x2 + 60 = 0 => x2 = -60
2. x2 - 20 = 0 => x2 = 20

Now that we have two possible values for x2, we can find the corresponding values for x1 using equation (1):

1. For x2 = -60: x1 = -40 - (-60) = -40 + 60 = 20

2. For x2 = 20: x1 = -40 - 20 = -60

So, the solutions for the variables are: x1 = 20, x2 = -60 or x1 = -60, x2 = 20