The product of two consecutive positive odd numbers is 1,023. find the numbers.

The two consecutive odd numbers whose product is 1,023 are 31 and 33

Let

Small odd number = x

Large odd number = x + 2

Product = x (x + 2)

Equation:

x(x + 2) = 1023

x² + 2x = 1023

x² + 2x - 1023 = 0

x² + 33x - 31x - 1023

(x + 33)(x - 31) = 0

x + 33 = 0 or x - 31 = 0

x = -33 or x = 31

We only consider the positive number since the odd number is positive

So,

x = 31

x + 2 = 33

Therefore, the two consecutive odd number whose product is 1023 are 31 and 33

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31, 33

Step-by-step explanation:

Let x = smaller odd number.

Then the next greater consecutive odd number is x + 2.

Their product is x(x + 2).

Their product equals 1023.

x(x + 2) = 1023

x^2 + 2x = 1023

x^2 + 2x - 1023 = 0

(x + 33)(x - 31) = 0

x + 33 = 0 or x - 31 = 0

x = -33 or x = 31

We discard the negative answer since we are told both numbers are positive.

x = 31

x + 2 = 33

The numbers are 31 and 33.

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