Question

The product of two consecutive odd numbers is 6723 what is the greater number

Answer 1

let a number be x

the other number is x+2

$x(x + 2) = 6723 \\ {x}^{2} + 2x = 6723 \\ {x}^{2} + 2x - 6723 = 0 \\ {x}^{2} + 83x - 81x - 6723 = 0 \\ x(x + 83) - 81(x + 83) = 0 \\ (x + 83) \: (x - 81) = 0 \\ x + 83 = 0 \: \: x - 81 = 0 \\ x = - 83 \: \: \: \: \: \: \: x = 81$

therefore first number is x = 81

2nd number x+2=81+2=83

the greater number is 83