Question

Prove that 1 added to the product of two even numbers is a perfect square.​

Answer 1

Answer:

This is not true. The product of any 2 even numbers will not be a perfect square. Let's take an example. 2×6=12 and 12+1=13. 13 is not a perfect square. Instead, the question should've been " Prove that 1 added to the product of 2 consequent even numbers is a perfect square."

Step-by-step explanation:

let the 2 numbers be n and n+2

the product is

n(n+2)

=$n^{2}$+2n

adding 1 to the product

= $n^{2}$+2n+1

now, we see that the above equation is in the form of $(a+b)^{2}=a^2+b^2+2ab$

=$(n+1)^{2}$

∴this will always be a perfect square.