Вопрос школьника по предмету Алгебра
1. Площа прямокутника 112 сантиметрів квадратних. Знайти сторони прямокутника, якщо одна з них на 9 см більша другої.
Ответ учителя по предмету Алгебра
Пусть одна сторона х см, тогда вторая равна (х + 9) см.
х(х + 9) = 112
х² + 9х — 112= 0
D = 9² — 4 · 1 · (-112) = 81 + 448 = 529; √529 = 23
x₁ = (-9 — 23)/2 = — 16 — не подходит по условию задачи
х₂ = (-9 + 23)/2 = 7
Значит, одна сторона прямоугольника равна 7 см, а вторая 7 + 9 = 16 (см)
Ответ: 7 см и 16 см.
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