Question

Find two consecutive odd integers whose product is 99.

Answer 1

Answer:

Hint: Consecutive odd numbers follow the form: x, x+2, x+4, so if "The product of two consecutive odd integers is 99".

Step-by-step explanation:

1st = 2x-1

2nd = 2x+1

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Equation:

(2x-1)(2x+1) = 99

4x^2-1 = 99

4x^2 = 100

x^2 = 25

x = 5 or -5

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If x = 5

2x-1 = 9

2x+1 = 11

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If x = -5

2x-1 = -11

2x+1 = -9

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Answer 2

Answer: Consecutive odd numbers are 9 and 11 or -9 and - 11.

Concept : Consecutive odd numbers

Given : Product of two consecutive odd numbers is 99.

To Find : The consecutive odd numbers

Step-by-step explanation:

In Mathematics, odd numbers are represented as (2n + 1).

Let the two consecutive odd numbers be (2n + 1) and (2n - 1).

According to the question :

⇒ (2n + 1)(2n - 1) = 99

⇒ $(4n^{2} - 2n + 2n - 1 ) = 99$

⇒ $4 n^{2} - 1 = 99$

⇒ $4 n^{2} = 100$

⇒ $n^{2} = 25$

∴ n = 5, -5

If n = 5 :

Then consecutive odd numbers are :

2n - 1 = 9 and 2n + 1 = 11

If n = -5 :

Then consecutive odd numbers are :

2n -1 = - 11 and 2n + 1 = - 9.

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