Question 230534: whats the answer to this.
the sum of the squares of two consecutive odd integers is 173. find the integers Found 2 solutions by jsmallt9, Alan3354:Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! First of all, the information you have provided is incorrect. The problem you have given has no solutions. This is because:
The square of any odd number is also odd.
Adding any two odd numbers always results in an even number.
173 is odd
So it is impossible for the sum of two odd numbers to add up to another odd number.
So either the 173 should be even or the two (consecutive odd numbers) should be odd. I will go as far as I can with the incorrect information and hope that it will help you figure out how to do the correct problem.
Consecutive odd integers are 2 apart from each other. (This may seem wrong initially but think about some odd integers and it will become clear that they are 2 apart from each other.) Now we can write expressions for our two consecutive odd integers:
Let x = the smaller odd integer
then
= the square of the smaller odd integer
(x+2) = the next (larger) odd integer
= the square of the second odd integer
= the sum of the squares of the two consecutive odd integers.
From the information in the problem we know that:
This is a quadratic equation (because of the terms) so we will solve this by simplifying:
... getting one side equal to zero...:
... and then factoring (or using the quadratic formula).
And here is where we get stuck because the problem you've given is incorrect. This does not factor and the quadratic formula comes up with irrational, not odd, answers. Once you correct the problem, I hope the above will be a help to you in solving it.
You can put this solution on YOUR website! the sum of the squares of two consecutive odd integers is 173. find the integers
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This is not possible.
The square of an odd number is an odd number.
Any 2 odd numbers add to an even number, so it can't be 173.
Any 2 even numbers also add to an even number, so there are no integers that do this.
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x^2 + (x+2)^2 = 173
2x^2 + 4x + 4 = 173
2x^2 + 4x - 169 = 0
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