Предмет: Алгебра, автор: vanyok75

1)Система 3y-x=4
x^2-4xy-2y^2=3

2)система 4y^2-12xy+9x^2=16
4y+5x=14

Ответы

Автор ответа: Аноним

0

Объяснение:

В первой системе очень удобно выразить х, и подставить во второе уравнение. После чего открываем скобки и приводим подобное.

Получаем квадратное уравнение, я умножила всё на -1 чтобы было удобнее.

Можно воспользоваться теоремой Виета, дискриминантом и т.д

Я для раскрытия квадратного многочлена использую такую формулу

$(ka^{2}+ ba+c)=(a+x_{1} )(a+x_{2} ) \\x_{1} + x_{2} = b \\x_{1} x_{2} =kc$

при этом, если k>0 уравнение следует записать в таком виде

$ka^{2}+x_{1}a+ x_{2}a+c$

и только потом выносить общий множитель за скобку.

В первом уравнении второй системы у нас разность квадрата, после того как мы нашли ее, можем возвести правую и левую части в корень, и извлечь его. После этого выражаем одну переменную через другую и ищем корни уравнения.

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