Номер 9 гдз 8 класс алгебра Муравин Муравина

Номер 9

 

у3 + 3у2 + 3у + 1 - у2 - 3у2 - 2,25у = 7 \begin{equation} 1)(y+1)^{3}- \end{equation} \begin{equation} -\frac{y}{4}(2y+3)^{2}=7 \end{equation} \begin{equation} y^{3}+3y^{2}+3y+1- \end{equation} \begin{equation} -\frac{y}{4}(4y^{2}+12y+9)=27 \end{equation} \begin{equation} y^{3}+3y^{2}+3y+ \end{equation} \begin{equation} +1-\frac{y}{4}\cdot 4y^{2}-\frac{y}{4}\cdot \end{equation} \begin{equation} \cdot 12y-\frac{y}{4}\cdot 9=7 \end{equation} 0,75у + 1 = 7
0,75у = 7 - 1
0,75у = 6 \begin{equation} y=\frac{6}{0,75} \end{equation} у = 8;
2) (8х - 3)2х - (4х - 1)3 = 7
(64х2 - 48х + 9)х - (64х3 -
- 48х2 + 12х - 1) = 7
64х3 - 48х2 + 9х - 64х3 +
+ 48х2 - 12х + 1 = 7
-3х = 6
х = -2; \begin{equation} 3)(2x-\frac{1}{3})^{3}- \end{equation} \begin{equation} -x\cdot (2x-\frac{1}{3})^{2}=0 \end{equation} \begin{equation} (2x-\frac{1}{3})^{2}\cdot (2x- \end{equation} \begin{equation} -\frac{1}{3}-x)=0 \end{equation} \begin{equation} (2x-\frac{1}{3})^{2}\cdot (x-\frac{1}{3})=0 \end{equation} \begin{equation} (2x-\frac{1}{3})^{2}=0 \end{equation} \begin{equation} 2x-\frac{1}{3}=0 \end{equation} \begin{equation} 2x=\frac{1}{3} \end{equation} \begin{equation} x=\frac{1}{3}:2 \end{equation} \begin{equation} x=\frac{1}{6} \end{equation} \begin{equation} или x-\frac{1}{3}=0 \end{equation} \begin{equation} x=\frac{1}{3}. \end{equation} \begin{equation} Ответ: x_{1}=\frac{1}{6};x_{2}=\frac{1}{3} \end{equation} 4) (4у - 3)3 - у(8у - 9)2 = 0
64у3 - 144у2 + 108у -
- у(64у2 - 144у + 81) = 0
64у3 - 144у2 + 108у -
- 64у3 + 144у2 - 81у = 0
27у = 0
у = 0;
5) х3 + 3х2 + 3х + 1 = 0
(х + 1)3 = 0
х + 1 = 0
х = -1;
6) 8у3 - 36у2 + 54у - 27 = 0
(2у - 3)3 = 0
2у - 3 = 0
2у = 3 \begin{equation} y=\frac{3}{2} \end{equation} или у = 1,5.

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