Решить систему уравнений: [latex] \left \{ {{2(x+y)=26} \atop {xy=30}} \right. [/latex]

[latex] \left \{ {{2(x+y) = 26} \atop {xy = 30}} \right. [/latex] [latex] \left \{ {x+y = 13} \atop {xy = 30}} \right. [/latex] [latex] \left \{ {y = 13-x} \atop {x(13-x) = 30}} \right. [/latex] [latex] \left \{ {y = 13-x} \atop {13x - x^2 = 30}} \right. [/latex] [latex] \left \{ {y = 13-x} \atop {13x - x^2 - 30= 0}} \right. [/latex] [latex] \left \{ {y = 13-x} \atop {x^2 -13x + 30}=0} \right. [/latex] Решим второе квадратное уравнение по обратной теореме Виета: x₁ + x₂ = 13 x₁*x₂ = 30 x₁ = 3 x₂ = 10 [latex] \left \{ {{y = 13 - x} \atop {x=3}} \right. [/latex] [latex] \left \{ {{y = 13 - x} \atop {x=10}} \right. [/latex] [latex] \left \{ {{y = 10} \atop {x=3}} \right. [/latex] [latex]\left \{ {{x = 10} \atop {y=3}} \right. [/latex] Ответ: [latex](10; 3), (3; 10).[/latex]

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