1)
xy = - 3
x^2y^2 = 9
y^2 = 9 / x^2
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4x^2 + y^2 = 13
4x^2 + ( 9 / x^2 ) = 13
4x^4 + 9 = 13x^2
4x^4 - 13x^2 + 9 = 0
x^2 = a ; a > 0
4a^2 - 13a + 9 = 0
D = 169 - 144 = 25 = 5^2
a1 = ( 13 + 5 ) : 8 = 2,25
a2 = ( 13 - 5 ) : 8 = 1
x^2 = a
x1 = 1,5
x2 = - 1,5
x3 = 1
x4 = - 1
y^2 = 9 / x^2
y^2 = 9 / 2,25 = 4
y1 = 2
y2 = - 2
y^2 = 9 / 1 = 9
y3 = 3
y4 = - 3
ОТВЕТ ( 1,5 ; 2 ) ; ( - 1,5 ; - 2 ) ; ( 1 ; 3 ) ; ( - 1 ; - 3 )
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2)
общий знаменатель x^2 - y^2 = ( x - y )( x + y )
( x + y )^2 - 2( x - y )^2 = x^2 - y^2
x^2 + 2xy + y^2 - 2( x^2 - 2xy + y^2 ) = x^2 - y^2
x^2 + 2xy + y^2 - 2x^2 + 4xy - 2y^2 = x^2 - y^2
- x^2 + 6xy - y^2 = x^2 - y^2
2x^2 - 6xy = 0
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x^2 - 5xy + 2y^2 = 4
x^2 = 5xy - 2y^2 + 4
2x^2 = 10xy - 4y^2 + 8
6xy = 10xy - 4y^2 + 8
4xy = 4y^2 - 8
xy = 2y^2 - 2
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2x^2 = 6xy
2x^2 = 6( 2y^2 - 2 )
2x^2 = 12y^2 - 12
x^2 = 6y^2 - 6
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x^2 - 5xy + 2y^2 = 4
6y^2 - 6 - 5( 2y^2 - 2 ) + 2y^2 = 4
6y^2 - 6 - 10y^2 + 10 + 2y^2 = 4
- 2y^2 + 4 = 4
y = 0
x^2 = - 6
ОТВЕТ нет решений