Предмет: Алгебра, автор: beata26

Решить задачу: У двух квадратов, сумма длин сторон которых 18 см, разность площадей которых равна 36 см^2. Вычислить длину сторон квадрата.


smorodinkalolp0t266: Точно цифры указаны верно вопрос

Ответы

Автор ответа: mishsvyat
0

Ответ:

8 и 10

Объяснение:

Обозначим длину стороны меньшего квадрата x, длину стороны большего квадрата y. Тогда условие для длины запишется как:

x+y=18 , а условие для площадей: y^2-x^2=36. Составим и решим систему уравнений:

\left \{ {{x+y=18} \atop {y^2-x^2=36}} \right. \rightarrow \left \{ {{x+y=18} \atop {(y+x)(y-x)=36}} \right. \rightarrow \left \{ {{x+y=18} \atop {18(y-x)=36}} \right. \rightarrow \left \{ {{x+y=18} \atop {y-x=2}} \right. \rightarrow \left \{ {{x=8} \atop {y=10}} \right.

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