Question : If the sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.
Option 1: 4
Option 2: 8
Option 3: 1
Option 4: 2
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Correct Answer: 2
Solution :
Given:
The sum of squares of two numbers = 12
Product of the numbers = 4
Let the numbers be $a$ and $b$.
⇒ $a^2+b^2=12$ and $ab = 4$
We know, $(a-b)^2=a^2+b^2-2ab$
⇒ $(a-b)^2=12-2\times4$
⇒ $(a-b)^2=12-8$
⇒ $(a-b)^2=4$
⇒ $a-b=\sqrt4=2$
Hence, the correct answer is 2.
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