x + y = - 6
xy = 5
Решение
x = - 6 - y
y( - 6 - y ) = 5
- 6y - y² = 5
y² + 6y + 5 = 0
D = 36 - 20 = 16 = 4²
y1 = ( - 6 + 4 ) : 2 = - 1
y2 = ( - 6 - 4 ) : 2 = - 5
x1 = - 6 + 1 = - 5
x2 = - 6 + 5 = - 1
ОТВЕТ ( - 5 ; - 1 ) ; ( - 1 ; - 5 )
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x² + y² = 34
x - y = - 2
Решение
x = y - 2
( y - 2 )² + y² = 34
y² - 4y + 4 + y² = 34
2y² - 4y - 30 = 0
2( y² - 2y - 15 ) = 0
D = 4 + 60 = 64 = 8²
y1 = ( 2 + 8 ) : 2 = 5
y2 = ( 2 - 8 ) : 2 = - 3
x1 = 5 - 2 = 3
x2 = - 3 - 2 = - 5
ОТВЕТ ( 3 ; 5 ) ; ( - 5 ; - 3 )
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9x² + y² = 9
6xy = 7
Решение
xy = 7/6 ==> y = 7 / 6x
9x² + ( 7 / 6x )² = 9
9x² + ( 49/36x² ) = 9
9x²*36x² + 49 = 9 * 36x²
9x²*36x² - 9*36x² + 49 = 0
324x⁴ - 324x² + 49 = 0
324x² = a
a² - a + 49 = 0
D = 1 - 196 = - 195 ( < 0 )
Нет решений