Question : Directions: There are two numbers. The difference between these two numbers is 2 and the difference between their squares is 8. What are those numbers?
Option 1: 12, 10
Option 2: 3, 1
Option 3: 7, 5
Option 4: 8, 6
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Correct Answer: 3, 1
Solution :
Given:
Let the two numbers be a and b.
The difference between these two numbers is 2.
⇒ a – b = 2 ———— (1)
And the difference between their squares is 8.
⇒ a
2
– b
2
= 8
As we know that a
2
– b
2
= (a – b)(a + b)
Now, put the value of (a
2
– b
2
) and (a – b) in a
2
– b
2
= (a – b)(a + b).
⇒ a
2
– b
2
= 2(a + b)
⇒ 8 = 2(a + b)
⇒ 4 = a + b ———— (2)
Now, add the equations (1) and (2) –
⇒ a – b + a + b = 2 + 4
⇒ 2a = 6
⇒ a = 3
Now, put the value of a in equation (1) –
⇒ a – b = 2
⇒ 3 – b = 2 ⇒ b = 1
So, the value of a is 3 and b is 1. Hence, the second option is correct.
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