Question of the day - 1

Q ) How many pair of natural numbers are such that difference between their squares is 39?


Options:

• 1
• 2
• 3
• 4

Now before you proceed further, just try to solve it by your own. Kindly post your solution in comment area. There are always many different ways in which question can be cracked but here we will see the shortest and most efficient method. If you have any better method, your suggestions are welcome. 

Solution:

Natural numbers are all positive numbers greater then 0.

A² - B² = 39
(A-B) (A+B) = 39

Now 39 can be factorized as

• 1 * 39
• 3 * 13
• 13 * 3
• 39 * 1

So we get for cases:

Case 1 :

A - B = 1

A + B = 39

So A = 20 and B = 19

Case 2:

A - B = 39

A + B = 1

So A = 20 and B = -19

Case 3:

A - B = 3

A + B = 13

So A = 8 and B = 5

Case 4:

A - B = 13

A + B = 3

A = 8 and B = -5

Now from all the above four cases, only two are positive pairs. So our answer is two. Option 2.

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