Find all order pairs (x,y) such that 2x^4 +5x^3 y +45xy^3 = 34x^2 y^2 + 18y^4 and 2x - 3y =7?

1 Answer
Jun 6, 2017

(-7,-7) and (14/5,-7/15)

Explanation:

2 x^4 + 5 x^3 y + 45 x y^3 - (34 x^2 y^2 + 18 y^4)=(2 x - 3 y) (x - y)^2 (x + 6 y) = 0

so solving

{(x-y=0),(2 x - 3 y=7):} and

{(2 x - 3 y=7),(x+6y=0):}

we get the pairs

(-7,-7) and (14/5,-7/15)