Question

Three cosecutive odd natural numbers are such that the product of the first and third is greater than four times the middle by 1. Find the number?​

Answer 1

Answer:

3, 5 ,7

Step-by-step explanation:

let the 3 consecutive odd natural numbers be 2x+1, 2x+3 and 2x+5.

now, as per the question,

(2x+1)(2x+5) = 4(2x+3)+1

4x² + 12x + 5 = 8x + 13

4x² + 4x - 8 = 0

4x² + 8x - 4x - 8 = 0

4x(x+2) - 4(x+2) = 0

(4x-4) (x+2) =0

x = 1(odd) or x= -2(even)

hence the numbers are:

2x+1 = 2*1+1 = 3

2x+3 = 2*1+3 = 5

2x+5 = 2*1+5 = 7

To check and confirm,

3*7 = 4(5) +1

21 = 21