+128406 x + y = 9/2, 2x^2 y^2 - 13xy + 18 = 0
2x^2y^2 - 13xy + 18 = 0 factor as
(2xy - 9 ) (xy - 2) = 0
Settting each factor to 0 and solving we have
2xy - 9 = 0 xy - 2 = 0
xy = 9/2 xy = 2
y = [9]/ [ 2x] y = 2/x
And using x + y = 9/2 we can solve this
x + [9] / [2x] = 9/2 multiply through by 2x
2x^2 + 9 = (9/2)(2x) rearrange
2x^2 - 9x + 9 = 0
(2x - 3) ( x - 3) = 0
So
2x - 3 =0 x - 3 = 0
x = 3/2 x = 3
And y = 9 ] [ 2(3/2)] = 3 And y = 9/ {2*3] = 3/2
So....two solutions are ( 3/2, 3) and ( 3 , 3/2)
And for the other solutions, we have that
x + 2/x = 9/2 multiply through by x
x^2 + 2 = (9/2)x
2x^2 - 9x + 4 = 0
(2x - 1) ( x - 4) = 0
2x - 1 = 0 x - 4 =0
x =1/2 x = 4
And y = 2/ [1/2] = 4 And y = 2 / 4 = 1/2
So....the other two solutions are (1/2, 4) and ( 4, 1/2)
