Question

Даю 30 балов.
$\left \{ {{\frac{x}{y} }-\frac {y}{x} = \frac{3}{2} } \atop {x-y=1}} \right.$

Answer 1

( 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 )

Answer 2

( x / y ) - ( y / x ) = 3/2
( x / y )=t
t-1/t = 3/2
t^2-3t/2-1=0
d=9/4+4=25/4
t1=(3/2+5/2)/2=2
t2=(3/2=5/2)/2=-1/2
************
x/y=2
x=2y
x-y=1
2y-y=1
x=2 y=1
*********
x/y=-1/2
y=-2x
x-y=1
x+2x=1
x=1/3 y=-2/3
*******
ответ (2;1) ; (1/3;-2/3)