$\dfrac{(x + y)^4}{(x - y)^4} = \dfrac{16}{1}$

Assertion (A) : x : y = 3 : 1

Reason (R) : $\dfrac{x + y}{x - y} = \dfrac{2}{1}$ and $\dfrac{x + y + x - y}{x + y - x + y} = \dfrac{2 + 1}{2 - 1}$

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is the correct reason for R.

4. Both A and R are true and R is the incorrect reason for R.

Both A and R are true and R is the correct reason for R.

Reason

Given,

$\Rightarrow \dfrac{(x + y)^4}{(x - y)^4} = \dfrac{16}{1}\\[1em] \Rightarrow \dfrac{(x + y)}{(x - y)} = \sqrt[4]{\dfrac{16}{1}}\\[1em] \Rightarrow \dfrac{(x + y)}{(x - y)} = \dfrac{2}{1}\\[1em] \Rightarrow \dfrac{(x + y) + (x - y)}{(x + y) - (x - y)} = \dfrac{2 + 1}{2 - 1}\\[1em] \Rightarrow \dfrac{x + y + x - y}{x + y - x + y} = \dfrac{3}{1}\\[1em] \Rightarrow \dfrac{2x}{2y} = \dfrac{3}{1}\\[1em] \Rightarrow \dfrac{x}{y} = \dfrac{3}{1}$

According to Assertion; x : y = 3 : 1 , which is true.

According to Reason; $\dfrac{x + y}{x - y} = \dfrac{2}{1}$ and $\dfrac{x + y + x - y}{x + y - x + y} = \dfrac{2 + 1}{2 - 1}$, which is true.

Hence, option 3 is the correct option.