x² + 3xy + y² = 11
2x + y = 3
Решение
y = 3 - 2x
y² = 9 - 12x + 4x²
x² + 3x( 3 - 2x ) + 9 - 12x + 4x² = 11
5x² - 12x + 9 - 9x - 6x² = 11
x² + 12x + 2 = 0
D = 144 - 8 = 96 ; √ D = √ ( 16*6 ) = 4√6
x1 = ( - 12 + 4√ 6 ) : 2 = ( - 6 + 2 √ 6 )
x2 = ( - 12 - 4√ 6 ) : 2 = ( - 6 - 2 √ 6 )
y1 = 3 - 2*( - 6 + 2√6 ) = 3 + 12 - 4√6 = 15 - 4√6
y2 = 3 - 2*( - 6 - 2√6 ) = 3 + 12 + 4√6 = 15 + 4√6
ОТВЕТ ( ( - 6 + 2√ 6) ; ( 15 - 4√ 6 ) ) ; ( ( - 6 - 2√6 ) ; ( 15 + 4√ 6 ))