Question

If the product of two consecutive odd integers is 255,find the integers

Answer 1

Answer:

the integers are = 15 & 17 or -17 & -15

Step-by-step explanation:

let 1 odd integer = 2x+1

other one = 2x+3

given, (2x+1)×(2x+3) = 255

=> 4x^2 + 6x + 2x + 3 - 255 = 0

=> 4x^2 + 8x - 252 = 0

=> x^2 + 2x - 63 = 0

=> x^2 + 9x - 7x -63 = 0

=> x(x+9) - 7(x+9) = 0

=> (x-7)(x+9) = 0

=> x-7 = 0 or x+9 = 0

=> x = 7 or -9

=> 2x+1 = 15 or -17

=> 2x+3 = 17 or -15