Given that x^2018 y^2017 = 1/2 and x^2016 y^2019 = 8

• Numbers

Given that x²⁰¹⁸y²⁰¹⁷ = 1/2 and x²⁰¹⁶y²⁰¹⁹ = 8, the value of x² + y³ is

1. 35/4
2. 37/4
3. 31/4
4. 33/4

Answer

x²⁰¹⁸y²⁰¹⁷ = 1/2

x²⁰¹⁶y²⁰¹⁹ = 8

Divide the two equations,

x²/y² = 1/16

x/y = 1/4

y = 4x

So, x²⁰¹⁶(4x)²⁰¹⁹ = 8

x⁴⁰³⁵ × 2⁴⁰³⁸ = 2³

x = 1/2

y = 2

Hence, x² + y³ = 1/4 + 8

= 33/4

The correct option is D.