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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 \[4\text{ }and\text{ }5.\]