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1. If x² + 4y² = 4xy, then x : y is -

A. 1 : 1

B. 1 : 2

C. 2 : 1

D. 1 : 4

Solution:

\begin{aligned} = x^{2} + 4 y^{2} = 4 x y \\ \Rightarrow x^{2} - 4 x y + 4 y^{2} = 0 \\ \Rightarrow (x - 2 y^{2}) = 0 \\ \Rightarrow x = 2 y \\ \Rightarrow \frac{x}{y} = 2 \\ \Rightarrow x : y = 2 : 1 \end{aligned}

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