Question

the sum of two consecutive natural numbers and the square of the first number is 5329 . What are the numbers

Answer 1

let the numbers be x and x+1
then
$x +x + 1 + {x}^{2} = 5329 \\ {x}^{2} + 2x + 1 = 5329 \\ {(x + 1)}^{2} = 5329 \\ x + 1 = 73 \\ it \: can \: not \: be \: - 73 \: because \: they \: are \: natural \: numbers \\ x = 72 \\ the \: number \: are \: 72 \: and \: 73$