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Дьяволтян
@Дьяволтян
July 2022
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Даю 30 балов.
[tex] \left \{ {{\frac{x}{y} }-\frac {y}{x} = \frac{3}{2} } \atop {x-y=1}} \right. [/tex]
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( x / y ) - ( y / x ) = 3/2 ; общий знаменатель 2xy ; X и Y не равны нулю ;2 Х^2 -2 Y^2 = 3XY ; X - Y = 1 ; Y = X - 1 ;2X^2 - 2 * ( X - 1 ) ^2 = 3X * ( X - 1 ) ;2X^2 - 2 * ( X^2 - 2X + 1 ) = 3X^2 - 3X ;2x^2 - 2x^2 + 4x - 2 = 3x^2 - 3x ;3x^2 - 7x + 2 = 0 ;D = 49 - 24 = 25 ; V D = 5 ;X1 = ( 7 + 5 ) : 6 = 2 ;X2 = ( 7 - 5 ) : 6 = 2/6 = 1/3 ;Y = Х - 1 ;Y1 = 2 - 1 = 1 ;Y2 = ( 1/3 ) - 1 = - ( 2/3 )ОТВЕТ ( 2 ; 1 ) ; ( 1/3 ; - 2/3 )
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( x / y ) - ( y / x ) = 3/2 ; общий знаменатель 2xy ; X и Y не равны нулю ;2 Х^2 -2 Y^2 = 3XY ; X - Y = 1 ; Y = X - 1 ;2X^2 - 2 * ( X - 1 ) ^2 = 3X * ( X - 1 ) ;2X^2 - 2 * ( X^2 - 2X + 1 ) = 3X^2 - 3X ;2x^2 - 2x^2 + 4x - 2 = 3x^2 - 3x ;3x^2 - 7x + 2 = 0 ;D = 49 - 24 = 25 ; V D = 5 ;X1 = ( 7 + 5 ) : 6 = 2 ;X2 = ( 7 - 5 ) : 6 = 2/6 = 1/3 ;Y = Х - 1 ;Y1 = 2 - 1 = 1 ;Y2 = ( 1/3 ) - 1 = - ( 2/3 )ОТВЕТ ( 2 ; 1 ) ; ( 1/3 ; - 2/3 )