Question

x2+xy+x=12 and y2+xy+y=18,find x-y

Answer 1

Hi ,

x² + xy + x = 12 ----( 1 )

y² + xy + y = 18 ----( 2 )

add equations ( 1 ) and ( 2 ) , we get

x² + 2xy + y² + x + y = 30

( x + y )² + ( x + y ) - 30 = 0

( x + y )² + 6( x + y ) - 5( x + y ) - 30 = 0

( x + y ) [ x + y + 6 ] - 5 ( x + y + 6 ) = 0

( x + y + 6 ) ( x + y - 5 ) = 0

Therefore ,

x + y + 6 = 0 or x + y - 5 = 0

x + y = -6 or x + y = 5