решите систему уравнений . Created by sasha0292. algebra-ru

решите систему уравнений ...

sasha0292 @sasha0292

July 2022 1 4 Report

решите систему уравнений

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$\displaystyle\bf\\\left \{ {{x^{2} -3xy-2y^{2}=2 } \atop {x+2y=1}} \right. \\\\\displaystyle\bf\\\left \{ {{(1-2y)^{2} -3(1-2y)y-2y^{2}=2 } \atop {x=1-2y}} \right. \\\\\displaystyle\bf\\\left \{ {{1-4y+4y^{2} -3y+6y^{2} -2y^{2}=2 } \atop {x=1-2y}} \right.\\\\\displaystyle\bf\\\left \{ {{8y^{2} -7y-1=0 } \atop {x=1-2y}} \right.\\\\\displaystyle\bf\\8y^{2} -7y-1=0\\\\\displaystyle\bf\\D=(-7)^{2} -4\cdot(-1)\cdot 8=49+32=81=9^{2}$

$\displaystyle\bf\\y_{1} =\dfrac{7-9}{16} =-\dfrac{2}{16}=-0,125 \\\\\displaystyle\bf\\y_{1} =\dfrac{7+9}{16} =\dfrac{16}{16}=1 \\\\\displaystyle\bf\\x_{1} =1-2y=1-2\cdot (-0,125)=1+0,25=1,25\\\\\displaystyle\bf\\x_{2} =1-2y=1-2\cdot 1=-1$

Ответ : (1,25 ; -0,125) , (- 1 ; 1)

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