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1. If x : y = 3 : 1, then x³ - y³ : x³ + y³ = ?

A. 13 : 14

B. 14 : 13

C. 10 : 11

D. 11 : 10

Solution:

\begin{aligned} x : y = 3 : 1 \\ ∴ \frac{x}{y} = \frac{3}{1} \\ ∴ \frac{x^{3} - y^{3}}{x^{3} + y^{3}} \\ \Rightarrow \frac{y^{3} (\frac{x^{3}}{y^{3}} - 1)}{y^{3} (\frac{x^{3}}{y^{3}} + 1)} \\ taking y^{3} common \\ = \frac{\frac{x^{3}}{y^{3}} - 1}{\frac{x^{3}}{y^{3}} + 1} \\ \Rightarrow \frac{27 - 1}{27 + 1} \\ \Rightarrow \frac{26}{28} \\ \Rightarrow \frac{13}{14} \end{aligned}

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