Question

решите способом подстановки систему уравнений
Х+7у=6
{
-2х+5х^2=12​

Answer 1

Ответ:

х+7у=6

х=6-7

х=1

________

7+6=13

13-7=6

Answer 2

Ответ:

$\bigg (\dfrac{7-\sqrt{2989}}{35}; \dfrac{203+\sqrt{2989}}{245} \bigg )\quad ; \quad \bigg (\dfrac{7+\sqrt{2989}}{35}; \dfrac{203-\sqrt{2989}}{245} \bigg ) \quad ;$

Объяснение:

$\displaystyle \left \{ {{x+7y=6} \atop {-2x+5x^{2}=12}} \right. \Leftrightarrow \left \{ {{x=6-7y} \atop {5 \cdot (6-7y)^{2}-2 \cdot (6-7y)-12=0}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{x=6-7y} \atop {5 \cdot (36-84y+49y^{2})-12+14y-12=0}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{x=6-7y} \atop {180-420y+245y^{2}+14y-24=0}} \right. \Leftrightarrow \left \{ {{x=6-7y} \atop {245y^{2}-406y+156=0}} \right. ;$

$245y^{2}-406y+156=0;$

$D=b^{2}-4ac;$

$D=(-406)^{2}-4 \cdot 245 \cdot 156=406^{2}-980 \cdot 156=(400+6)^{2}-(1000-20) \cdot 156=$

$=400^{2}+2 \cdot 400 \cdot 6+6^{2}-156000+3120=160000+4800+36-156000+3120=$

$=4000+4800+3156=4000+7956=11956;$

$11956=12000-44=4 \cdot (3000-11)=4 \cdot 2989;$

$y_{1,2}=\dfrac{-b \pm \sqrt{D}}{2a} \Rightarrow y_{1,2}=\dfrac{-(-406) \pm \sqrt{11956}}{2 \cdot 245}=\dfrac{406 \pm 2\sqrt{2989}}{2 \cdot 245}=\dfrac{203 \pm \sqrt{2989}}{245};$

$x=6-7y \Rightarrow x_{1,2}=6-\dfrac{7 \cdot (203 \pm \sqrt{2989})}{7 \cdot 35}=\dfrac{210-(203 \pm \sqrt{2989})}{35}=$

$=\dfrac{210-203 \mp \sqrt{2989}}{35}=\dfrac{7 \mp \sqrt{2989}}{35};$

$\bigg (\dfrac{7-\sqrt{2989}}{35}; \dfrac{203+\sqrt{2989}}{245} \bigg )\quad ; \quad \bigg (\dfrac{7+\sqrt{2989}}{35}; \dfrac{203-\sqrt{2989}}{245} \bigg ) \quad ;$