tex]...

daqqwe @daqqwe

July 2022 1 7 Report

Помогите, пожалуйста решить систему уравнений
[tex]\left \{ {{x^{2}+6y+9 =0} \atop {y^{2}+6x+9 =0}} \right.[/tex]

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AnonimusPro

Verified answer

вычтем из 1 уравнения 2 уравнение

$x^2+6y+9-y^2-6x-9=0\\x^2-y^2+6y-6x=0\\(x-y)(x+y)-6(x-y)=0\\(x-y)(x+y-6)=0\\1) x-y=0; \ x=y\\x^2+6x+9=0\\(x+3)^2=0\\x=-3\\y=-3\\(-3;3)\\2)x+y-6=0\\y=6-x\\x^2+6(6-x)+9=0\\x^2+36-6x+9=0\\x^2-6x+45=0\\D=36-4*45$

Ответ: (-3;-3)

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