Question : If the square of the sum of two numbers is equal to 4 times their product, then the ratio of these numbers is:
Option 1: 2 : 1
Option 2: 1 : 3
Option 3: 1 : 1
Option 4: 1 : 2
Correct Answer: 1 : 1
Solution : Let the numbers be $x$ and $y$. According to the question, $(x + y)^2 = 4xy$ ⇒ $x^2+y^2+2xy-4xy = 0$ ⇒ $x^2+y^2-2xy = 0$ ⇒ $(x -y)^{2} = 0$ ⇒ $x = y$ $\therefore$ The required ratio is 1 : 1. Hence, the correct answer is 1 : 1.
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