CAT 2018 Surds and Indices Question (Hard)

Question

Given that and , the value of ?

Accepted Answer

Step 1 Divide Eq. 1 by Eq. 2 cdot y 2017 x 2016 cdot y 2019 2 8 Simplifying the exponents x 2018 - 2016 cdot y 2017 - 2019 x 2 cdot y -2 Simplifying RHS 2 div 8 2 cdot 8 16 Thus, the equation becomes x 2 cdot y 2 16 quad Longrightarrow quad y 2 16 Take square roots y 4 quad Longrightarrow quad x 4 -

CAT 2018

Quantitative

Surds and Indices

Hard

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

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