Решить систему уравнений: [tex] \left \{ {{2(x+y)=26} \atop {xy=30}} \right. [/tex]. Created by Женя123. algebra-ru

tex]...

Verified answer

$\left \{ {{2(x+y) = 26} \atop {xy = 30}} \right.$

$\left \{ {x+y = 13} \atop {xy = 30}} \right.$

$\left \{ {y = 13-x} \atop {x(13-x) = 30}} \right.$

$\left \{ {y = 13-x} \atop {13x - x^2 = 30}} \right.$

$\left \{ {y = 13-x} \atop {13x - x^2 - 30= 0}} \right.$

$\left \{ {y = 13-x} \atop {x^2 -13x + 30}=0} \right.$

Решим второе квадратное уравнение по обратной теореме Виета:

x₁ + x₂ = 13
x₁*x₂ = 30

x₁ = 3
x₂ = 10

$\left \{ {{y = 13 - x} \atop {x=3}} \right.$

$\left \{ {{y = 13 - x} \atop {x=10}} \right.$

$\left \{ {{y = 10} \atop {x=3}} \right.$

$\left \{ {{x = 10} \atop {y=3}} \right.$

Ответ: $(10; 3), (3; 10).$

2 votes Thanks 2

Answers & Comments

Verified answer

Verified answer

рекомендуемые вопросы

Helpful Links

Helpful Social