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Hidrargirum
@Hidrargirum
August 2022
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Решите систему уравнений
3х–у=–10
х²–4ху–у²=–20
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GREENDEY
3х–у
=–10
х²–4ху–у² = –20
у =
3х +
10
х²–4х(3х +10)–(
3х +10)
² = –20
Решаем второе уравнение:
х²–12х² – 40х – 9х²
– 60х
– 100 + 20 = 0
–20х² – 100х – 80 = 0
| : (-20)
х² + 5х + 4 = 0
По теор. Виета х1 + х2 = - 5, х1 * х2 = 4 =>
х1 = -1 => y1 =
3*(-1) +10
= 7
х2 = -4 => y2 = 3*(-4) +10 = -2
Ответ: (-1 ; 7), (-4; -2)
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Answers & Comments
х²–4ху–у² = –20
у =3х +10
х²–4х(3х +10)–(3х +10)² = –20
Решаем второе уравнение:
х²–12х² – 40х – 9х² – 60х – 100 + 20 = 0
–20х² – 100х – 80 = 0 | : (-20)
х² + 5х + 4 = 0
По теор. Виета х1 + х2 = - 5, х1 * х2 = 4 =>
х1 = -1 => y1 = 3*(-1) +10 = 7
х2 = -4 => y2 = 3*(-4) +10 = -2
Ответ: (-1 ; 7), (-4; -2)