Given that x^{2018}y^{2017} = 1/2 and x^{2016}y^{2019} = 8, the value of x^{2} + y^{3} is

- 35/4
- 37/4
- 31/4
- 33/4

### Answer

x^{2018}y^{2017} = 1/2

x^{2016}y^{2019} = 8

Divide the two equations,

x^{2}/y^{2} = 1/16

x/y = 1/4

y = 4x

So, x^{2016}(4x)^{2019} = 8

x^{4035} × 2^{4038} = 2^{3}

x = 1/2

y = 2

Hence, x^{2} + y^{3} = 1/4 + 8

= 33/4

**The correct option is D.**