We have, x4y4(x+y)=810 and
x3y3(x3+y3)=945 or x3y3(x+y)(x2−xy+y2)=945
On division, x2−xy+y2xy=945810=76
⇒xy−1+yx=76
Let, yx=v
So, 1v−1+v=76
⇒v+1v=76+1=136
Thus, 6v2+6=13v
⇒6v2−4v−9v+6=0
⇒(3v−2)(2v−3)=0
⇒v=32,23
Since, v=yx=32, y=3k & x=2k
So, (2k)4.(3k)4.(2k+3k)=810
⇒8k9=1
⇒k=121/3
Now, y=3k=3.2−1/3 and x=2k=2.2−1/3=22/3
When v=23, it can be shown that the values of x and y would interchange, that is x=3.2−1/3 and y=22/3.