Question

Given positive integers $x$ and $y$ such that $2x^2y^3 + 4y^3 = 149 + 3x^2$, what is the value of $x + y$?

Answer 1

Answer:

5

Step-by-step explanation:

2x²y³ + 4y³ = 149 + 3x²

$2x^2y^3 - 3x^2 = 149 - 4y^3$

$x^2(2y^3 - 3) = 149 - 4y^3$

$x^2 = \dfrac{149 - 4y^3}{2y^3 - 3}$

$x = \pm \sqrt{\dfrac{149 - 4y^3}{2y^3 - 3}}$

Try y = 1

$x = \pm \sqrt{\dfrac{149 - 4(1)}{2(1)^3 - 3}} = \pm \sqrt{-145} = i\sqrt{145}$

For y = 1, x is imaginary.

Try y = 2

$x = \pm \sqrt{\dfrac{149 - 4(2)^3}{2(2)^3 - 3}} = \pm \sqrt{9} = \pm 3$

Since x and y are positive integers, ignore x = -3.

When x = 3, y = 2.

x + y = 3 + 2 = 5