Решить систему уравнений [tex] \left \{ {{ x^{2}-xy+ y^{2} =7} \atop {x-y=1}} \right. [/tex]. Created by Tolianuch965. algebra-ru

Решим первое уравнение: или Ответ: (3; 2), (-2; -3)

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Tolianuch965 @Tolianuch965

July 2022 2 41 Report

Решить систему уравнений
[tex] \left \{ {{ x^{2}-xy+ y^{2} =7} \atop {x-y=1}} \right. [/tex]

DNHelper

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$\left \{ {{ x^{2}-xy+ y^{2} =7} \atop {x-y=1}} \right.$
$\left \{ {{(y+1)^2-y(y+1)+y^2=7} \atop {x=y+1} \right.$
Решим первое уравнение:
$y^2+2y+1-y^2-y+y^2=7$
$y^2+y-6=0$
$y = -3; 2$
$\left \{ {{x=3} \atop {y=2}} \right.$ или $\left \{ {{x=-2} \atop {y=-3}} \right.$

Ответ: (3; 2), (-2; -3)

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Universalka

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$\left \{ {{(1+y) ^{2} -y(1+y)+ y^{2} =7} \atop {x=1+y}} \right.$ 7

$\left \{ {{1+2y+ y^{2}-y- y^{2} +y ^{2} =7 } \atop {x=1+y}} \right.$

$\left \{ {{ y^{2}+y-6=0 } \atop {x=1+y}} \right.$
y = - 3 y = 2
x = 1 - 3 = - 2 x = 1 + 2 = 3
Ответ: (- 2 ; - 3) , ( 3 , 2)

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