What is the smallest positive number that must be added to the product of any two consecutive even numbers to make the result a perfect square?
Show answer & explanation
Correct answer: B
Explanation
Has been given :
Two consecutive even numbers = 2n, 2n + 2
According to the formula:
Product + k = perfect square
Product= 2n(2n + 2)= 4n² + 4n
Suppose k is added to it:
4n² + 4n + k
4n² + 4n + 1
= (2n + 1)²
Therefore
k = 1