4*(0.7х - 4) = 3*(0.2х + 6) - уравнение х*|х| = -4х - уравнение Помогите пожалуйста!. Created by Apppllll. matematika-ru

4*(0.7х - 4) = 3*(0.2х + 6) - уравнение х*|х| = -4х - уравнение Помогите пожалу...

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Ответ:

$1)\ \ 4\cdot (0,7x-4)=3\cdot (0,2x+6)\\\\2,8x-16=0,6x+18\\\\2,2x=34\\\\x=\dfrac{34}{2,2}\ \ ,\ \ \ x=\dfrac{340}{22}\ \ ,\ \ \ x=15\dfrac{5}{11}$

$2)\ \ x\cdot |x|=-4x\\\\a)\ \ x\geq 0:\ \ \ x\cdot x=-4x\ \ ,\ \ x^2+4x=0\ \ ,\ \ x\cdot (x+4)=0\ \ ,\\\\x_1=0\ ,\ x_2=-4\notin [\ 0\ ;+\infty )\\\\b)\ \ x$

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Соммон

$4*(0.7x - 4) = 3*(0.2x + 6);\\4*0,7x - 4*4 = 3*0,2x + 3*6;\\2,8x - 16 = 0,6x + 18;\\2,8x - 0,6x = 16 + 18;\\2,2x = 34;\\22x = 340;\\11x = 170;\\x = \frac{170}{11} = 15\frac{5}{11}.$

Ответ:

$x = 15\frac{5}{11}.$

$x*|x| = -4x.$

$\left[ \begin{gathered} \left\{ \begin{gathered} x\geq0, \hfill \\ x*x =-4x; \hfill \\ \end{gathered} \right. \hfill \\ \left\{ \begin{gathered} x< 0, \hfill \\ x*(-x) =-4x; \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \right.$

$\left[ \begin{gathered} \left\{ \begin{gathered} x\geq0, \hfill \\ x^{2} =-4x; \hfill \\ \end{gathered} \right. \hfill \\ \left\{ \begin{gathered} x< 0, \hfill \\ -x^{2} =-4x; \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \right.$

$\left[ \begin{gathered} \left\{ \begin{gathered} x\geq0, \hfill \\ x^{2}+4x=0; \hfill \\ \end{gathered} \right. \hfill \\ \left\{ \begin{gathered} x< 0, \hfill \\ -x^{2}+4x=0; \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \right.$

$\left[ \begin{gathered} \left\{ \begin{gathered} x\geq0, \hfill \\ x(x+4)=0; \hfill \\ \end{gathered} \right. \hfill \\ \left\{ \begin{gathered} x< 0, \hfill \\ -x(x-4)=0; \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \right.$

$\left[ \begin{gathered} \left\{ \begin{gathered} x\geq0, \hfill \\ x=0,\hfill \\ x=-4; \hfill \\ \end{gathered} \right. \hfill \\ \left\{ \begin{gathered} x< 0, \hfill \\ x=0; \hfill \\ x=4.\hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \right.$

В первой системе последней совокупности х не может быть -4, поскольку этот корень не удовлетворяет требованию х≥0. А во второй системе х не может быть равно ни 0, ни 4, так как х<0. Поэтому остается один корень: х=0.

Ответ:

$x=0.$

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