If 2a/y = (m² + n²)/mn, then √(a − y)/√(a + y) = ?

Correct answer: a (m−n)/(m+n)

From a/y = (m² + n²)/2mn, (a − y)/(a + y) = (m − n)²/(m + n)²; the root gives (m − n)/(m + n).

Why the other options are wrong

• b (m+n)/(m−n): This is inverted; a − y is on top so (m − n) goes on top.
• c √((m−n)/(m+n)): The root is misplaced; (a − y)/(a + y) is itself (m − n)²/(m + n)², so taking the root cancels the square.
• d √((m+n)/(m−n)): This is inverted with the root misplaced; the correct result is (m − n)/(m + n).