Find two consecutive odd numbers whose product is 399?

Answer 1

If one of the numbers is x, then the other number is x + 2. So,

x(x + 2) = 399

x^2 + 2x = 399 Complete the square by adding 1 at both sides ;

x^2 + 2x + 1 = 399 + 1 Use the formula: (a + b)^2 = a^2 + 2ab + b^2

(x + 1)^2 = 400

x + 1 = (+ & - )(square root of 400) subtract 1 to both sides

x = -1 (+ & -) 20

x = -1 + 20 or x = -1 - 20

x = 19 or x = -21

So,

x + 2 = 19 + 2 = 21 or x + 2 = - 21 + 2 = - 19

Thus the numbers are:

19 and 21 or -19 and - 21

Check:

(19)(21) = 399

(-19)(-21) = 399