Question

Решить систему уравнений X+4y=10 X( в квадрате)+xy=-2

Answer 1

X + 4y = 10 
x^2 + xy = - 2 
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x = 10 - 4y 
( 10 - 4y )^2 + y( 10 - 4y ) + 2 = 0 
100 - 80y + 16y^2 + 10y - 4y^2 + 2 = 0
12y^2 - 70y + 102 = 0 
2( 6y^2 - 35y + 51 ) = 0
D = 1225 - 1224 = 1 
y1 = ( 35 + 1 ) : 12 = 3
y2 = ( 35 - 1 ) : 12 = 17/6 = 2 5/6 
x1 = 10 - 4 * 3 = - 2 
x2 = 10 - 4 * ( 17/6 ) = 10 - (34/3 ) = 10 - 11 1/3 = - 1 1/3 
Ответ ( - 2 ; 3 ) ; ( - 1 1\3 ; 2 5\6 )