The sum of the squares of two consecutive natural numbers is 41. Find the numbers.
The sum of the squares of two consecutive natural numbers is 41. Find the numbers.

Allow us to take the two successive regular numbers as x and x + 1.

So from the inquiry,

\[x2\text{ }+\text{ }\left( x\text{ }+\text{ }1 \right)2\text{ }=\text{ }41\]

\[2×2\text{ }+\text{ }2x\text{ }+\text{ }1\text{ }\text{ }41\text{ }=\text{ }0\]

\[x2\text{ }+\text{ }x\text{ }\text{ }20\text{ }=\text{ }0\]

\[\left( x\text{ }+\text{ }5 \right)\text{ }\left( x\text{ }\text{ }4 \right)\text{ }=\text{ }0\]

\[x\text{ }=\text{ }-\text{ }5,\text{ }4\]

As – 5 is definitely not a characteristic number.

\[x\text{ }=\text{ }4\] is the main arrangement.

Along these lines, the two continuous normal numbers are \[4\text{ }and\text{ }5.\]