Question:
Given that x2018y2017 = 1/2 and x2016y2019 = 8, the value of x2 + y3 is
- 35/4
- 37/4
- 31/4
- 33/4
Correct Answer: 4
$x^{2018} y^{2017}=\frac{1}{2}$…..(1)
and $x^{2016} y^{2019}=8$…..(2)
Dividing (1) by (2), $\frac{x^{2}}{y^{2}}=\frac{1}{16}$
$\frac{x}{y}=\frac{1}{4}$ i.e. $x=\pm \frac{1}{4} y$
$\left(\pm \frac{1}{4} y\right)^{2018} y^{2017}=\frac{1}{2}$
$y^{4035}=2^{4035}$
$y=2$
Therefore, $x=\pm \frac{1}{4}y=\pm \frac{1}{2}$
Hence, $x^{2}+y^{3}=\frac{1}{4}+8=\frac{33}{4}$
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