The problem is as follows:
Let x and y be integers such that xy(x+y)=48 and xy+x+y=14. Calculate x^2+y^2.
Answer Choices:
(A) 13
(B) 16
(C) 20
(D) 40
(E) 68
So far I have come up that xy=48/(x+y) and I substitute that into the other equation making 48/(x+y)+x+y=14. After that I feel completely stuck,
If I multiply x+y to everything else I still end up with two variables leaving me nowhere. Still I do kind of know the answer. I looked at the multiple
choices and saw that 20 could be separated into 16 and 4 having roots of 4 and 2. 4 and 2 do indeed fit into both equations, but this method is
likely not going to help in other problems. If anyone can explain it would help me a great deal!
Let x and y be integers such that xy(x+y)=48 and xy+x+y=14. Calculate x^2+y^2.
Answer Choices:
(A) 13
(B) 16
(C) 20
(D) 40
(E) 68
So far I have come up that xy=48/(x+y) and I substitute that into the other equation making 48/(x+y)+x+y=14. After that I feel completely stuck,
If I multiply x+y to everything else I still end up with two variables leaving me nowhere. Still I do kind of know the answer. I looked at the multiple
choices and saw that 20 could be separated into 16 and 4 having roots of 4 and 2. 4 and 2 do indeed fit into both equations, but this method is
likely not going to help in other problems. If anyone can explain it would help me a great deal!