F.2 maths

a)
xy - 6x - 6y + 36
= x(y - 6) - 6y + 36
= x(y - 6) - 6(y - 6)
= (x - 6)(y - 6)
b)
xy=6(x+y) , x >= y
By a) : xy - 6x - 6y + 36
= xy - 6(x+y) + 36
= 36
So
(x - 6)(y - 6) = 36
(x - 6)(y - 6) = 2^2 * 3^2
When (x - 6) = 36 , (y - 6) = 1
x = 42 , y = 7
When (x - 6) = 18 , (y - 6) = 2
x = 24 , y = 8
When (x - 6) = 12 , (y - 6) = 3
x = 18 , y = 9
When (x - 6) = 9 , (y - 6) = 4
x = 15 , y = 10

2010-05-03 18:17:03 補充：
When (x - 6) = 6 , (y - 6) = 6

x = 12 , y = 12

2010-05-03 18:23:31 補充：
Yes!

Thank you vyctang!!

博士 : missing one solution for 6 x 6

then x = 12 and y = 12