Question

Решите систему уравнений :$left { {{x^2+3xy+y^2=11} atop {2x+y=3}} right.$

Answer 1

 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 ))