( x/y ) + ( y/x ) = 5/2
X + y = 6
Решение
у = 6 - Х
( Х/( 6 - Х )) + ( ( 6 - Х )/Х ) = 5/2
( х^2 + ( 6 - Х )^2 ) / ( х( 6 - Х )) = 5/2
( х^2 + 36 - 12х + х^2 ) / ( 6х - х^2 ) = 5/2
( 2х^2 - 12х + 36 ) /( 6х - х^2 ) = 5/2
2( 2х^2 - 12х + 36 ) = 5( 6х - х^2 )
4х^2 - 24х + 72 = 30х - 5х^2
9х^2 - 54х + 72 = 0
9( х^2 - 6х + 8 ) = 0
D = 36 - 32 = 4 = 2^2
X1 = ( 6 + 2 ) : 2 = 4
X2 = ( 6 - 2 ) : 2 = 2
у = 6 - Х
у1 = 6 - 4 = 2
у2 = 6 - 2 = 4
Ответ ( 4 ; 2 ) ; ( 2 ; 4 )