Question

\[\frac{(𝑥+𝑦)^4}{(𝑥−𝑦)^4} =\frac{16}1\].

Assertion (A): 𝑥 : 𝑦 = 3 : 1.

Reason (R): \[\frac{𝑥 + 𝑦}{𝑥−𝑦} = 21\] and \[\frac{𝑥+𝑦+𝑥−𝑦} {𝑥+𝑦−𝑥+𝑦} = \frac{2 + 1}{2−1}.\]

Options

• A is true, R is false.

• A is false, R is true.

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

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

Answer 1

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

Explanation:

Given,

\[\Rightarrow \frac{(x + y)^{4}}{(x - y)^{4}} = \frac{16}{1}\]

\[\Rightarrow \frac{(x + y)}{(x - y)} = \sqrt[4]{\frac{16}{1}}\]

\[\Rightarrow \frac{(x + y)}{(x - y)} = \frac{2}{1}\]

\[\Rightarrow \frac{(x + y) + (x - y)}{(x + y) - (x - y)} = \frac{2 + 1}{2 - 1}\]

\[\Rightarrow \frac{x + y + x - y}{x + y - x + y} = \frac{3}{1}\]

\[\Rightarrow \frac{2x}{2y} = \frac{3}{1}\]

\[\Rightarrow \frac{x}{y} = \frac{3}{1}\]

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

According to Reason; \[\frac{𝑥 + 𝑦}{𝑥−𝑦} = 21\] and \[\frac{𝑥+𝑦+𝑥−𝑦} {𝑥+𝑦−𝑥+𝑦} = \frac{2 + 1}{2−1}.\] which is true.