Question

Решение систем уравнений второй степени

Answer 1

- 3x^2 - 9y^2 = - 156
x - 6y = 13
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- 3( x^2 + 3y^2 ) = - 3•52
x^2 + 3y^2 = 52
x^2 = 52 - 3y^2
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X = 13 + 6y
X^2 = 169 + 156y + 36y^2
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169 + 156y + 36y^2 = 52 - 3y^2
39y^2 + 156y + 117 = 0
13( 3y^2 + 12y + 9 ) = 0
3( y^2 + 4y + 3 ) = 0
D = 16 - 12 = 4 = 2^2
y1 = ( - 4 + 2 ) : 2 = - 1
y2 = ( - 4 - 2 ) : 2 = - 3
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X = 13 + 6y
X1 = 13 - 6 = 7
X2 = 13 - 18 = - 5
Ответ ( 7 ; - 1 ) ; ( - 5 ; - 3 )