Question

The product of 2 consecutive odd integers is 483

Answer 1

Let the first odd number be 2x+1
Then the consecutive odd no =(2x+1)+2=2x+3
ATQ
(2x+1)(2x+3)=483
$4{x}^{2} + 6x + 2x + 3 = 483 \\ 4 {x}^{2} + 8x - 483 + 3 = 0 \\ 4 {x}^{2} + 8x - 480 = 0 \\ {x}^{2} + 2x - 120 = 0 \\ {x}^{2} + 12x - 10x - 120 = 0 \\ x(x + 12) - 10(x + 12) = 0 \\ (x + 12)(x - 10) = 0 \\ x = - 12 \: \: \: \: \: or \: \: \: \: \: x = 10 \\ x = - 12 \: is \: not \: possible \\ so \: x = 10$
First odd no =2x+1=2×10+1=21
Second odd no =21+2=23