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Question
The difference of the squares of two consecutive even natural numbers is 68. Find the two numbers.
Solution
Let the two consecutive even natural numbers be 2x and 2x + 2.
As per the given condition,
(2x + 2)2 - (2x)2 = 68
⇒ 4x2 + 8x + 4 - 4x2 = 68
⇒ 8x + 4 = 68
⇒ 8x = 64
⇒ x = `(64)/(8)`
⇒ x = 8
2x = 2(8)
= 16 and 2x + 2
= 2(8) + 2
= 16 + 2
= 18
Hence, the numbers are 16 and 18.
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