Question

How do you find three consecutive odd integers such that the product of the two smaller exceeds the largest by 52?

Answer 1

let the numbers be x, x + 2, x + 4

x × (x + 2) = x + 4 + 52

x^2 + 2x = x + 56

${x}^{2} + x - 56 = 0 \\ {x}^{2} + 8x - 7x - 56 = 0 \\ x(x + 8) - 7(x + 8) = 0 \\ (x + 8)(x - 7) = 0 \\ x + 8 = 0 \: \: \: \: \: x - 7 = 0 \\ x = - 8 \: \: \: \: x = 7$

as the number is odd we take x = 7

the numbers are x, x+2, x+4

7, 9, 11