Three Consecutive Odd Integers

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In summary, the conversation was about finding three consecutive odd integers that satisfy the equation x^2 + (x + 4)^2 = 170. The solution involves setting up the equation correctly and solving for x, making sure the final answer is an odd integer.
  • #1
mathdad
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Find three consecutive odd integers such that the square of the first plus the square of the third is 170.

See picture for the set up.

View attachment 7356

Is the set up correct?
 

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  • #2
Re: Three Executive Odd Integers

RTCNTC said:
Find three consecutive odd integers such that the square of the first plus the square of the third is 170.

See picture for the set up.

Is the set up correct?
That's good. Just solve for x and make sure your answer is odd. Another addition to this would be to set x = 2n + 1, which forces x to be odd, but you don't actually have to take this step.

-Dan

Edit: Whoops! Your equation should only contain two numbers: \(\displaystyle x^2 + (x + 4)^2 = 170\). Sorry about that.
 
  • #3
Re: Three Executive Odd Integers

topsquark said:
That's good. Just solve for x and make sure your answer is odd. Another addition to this would be to set x = 2n + 1, which forces x to be odd, but you don't actually have to take this step.

-Dan

Edit: Whoops! Your equation should only contain two numbers: \(\displaystyle x^2 + (x + 4)^2 = 170\). Sorry about that.

Ok. Thanks.
 
  • #4

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  • #5
Re: Three Executive Odd Integers

RTCNTC said:
See picture reply.

Correct?
You switched signs. It's \(\displaystyle (x - 7)(x + 11) = x^2 + (-7 + 11)x - 77 = x^2 + 4x - 77\).

-Dan
 
  • #6
Re: Three Executive Odd Integers

I rushed through the problem. Thanks for the correction.
 

FAQ: Three Consecutive Odd Integers

1. What are three consecutive odd integers?

Three consecutive odd integers are three numbers that follow each other in sequence and are all odd. For example, 3, 5, and 7 are consecutive odd integers.

2. How can I find three consecutive odd integers?

To find three consecutive odd integers, you can start with any odd number and add 2 to it twice. For example, if you start with 3, you can add 2 to get 5 and then add 2 again to get 7, making 3, 5, and 7 consecutive odd integers.

3. What is the sum of three consecutive odd integers?

The sum of three consecutive odd integers is always a multiple of 3. For example, the sum of 3, 5, and 7 is 15, which is a multiple of 3.

4. Can there be negative consecutive odd integers?

Yes, there can be negative consecutive odd integers. For example, -3, -5, and -7 are consecutive odd integers.

5. What is the difference between consecutive odd integers?

The difference between consecutive odd integers is always 2. This is because each number is 2 more than the previous number. For example, the difference between 3 and 5 is 2, and the difference between 5 and 7 is also 2.

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