Given positive integers x and y such that 2x^2*y^3+4y^3=149+3x^2, what is the value of x+y?
2x^2*y^3+4y^3=149+3x^2
2y^3*x^2 - 3x^2 + 4y^3 - 149 = 0
(2y^3 - 3)x^2 + 4y^3 - 149 = 0
√ [ - 4(2y^3 - 3)(4y^3- 149) ] √ [ 4 (2y^3 - 3) (149 - 4y^3) ]
x = ________________________ = _________________________ =
2(2y^3 - 3) 2 ( 2y^3 - 3)
√ [ (2y^3 - 3) (149 - 4y^3)] √ [ (149 - 4y^3)]
= ______________________ = _____________
(2y^3 - 3) √ (2y^3 - 3)
Assuming that y is an integer > 1 .... if y = 2.... then x = √[ 117 / 13] = √9 = 3
So..(x, y) = (3, 2)