Question

three consecutive odd natural number are such that the product of the product of the first and third is greater than four times the middle by 1.find the number (solve using only one variable'x')​

Answer 1

Answer:

let three consecutive odd integers = x+2 , x , x-2

Now according to question

$(x + 2) \times (x - 2) - 4 \times x = 1 \\ {x}^{2} - {2}^{2} - 4 \times x = 1 \\ {x}^{2} - 4 - 4x = 1 \\ {x}^{2} - 4x - 5 = 0 \\ {x}^{2} - 5x + x - 5 = 0 \\ x(x - 5) + 1(x - 5) = 0 \\ (x + 1)(x - 5) = 0 \\ (x + 1) = 0 \: \: and \: \: (x - 5) = 0$

So x=-1 or x=5

NOW cosecutive odd numbers will be

if x=-1

1,-1 and -3

if x=5

7,5 and 3

HOPE IT HELPED