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x,y,z are three consecutive positive odd integers that satisfy y^2 - x^2 = 344. Find the value of z?

 

Work done:

 

(y+z) (y-z) = 344

 

(y+z) = 43

(y-z) = 4

 

y=4+z

 

y+z = 86

4+z+z = 86

2z = 82

z = 41

 

Where did I mess up? Says the answer is 89...? (didn't know the other way to say nail was censored, sorry!)

 Jan 1, 2021
edited by TheOddOne  Jan 1, 2021
 #1
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Hello TheOddOne (I love your profile picture)

 

The formula you used is x^2 - y^2 = (x+y)(x-y)

So  y^2 - x^2 = 344 is actually (y+x)(y-x) = 344. 

Since x = y + 2. 

Following your logic, y - x = 2 (consecutive odd number), so y + x = 172 (344/2). 

 

y = 85

x = 87

Which makes z 89.

 

I hope this helped. :)))

=^._.^=

 Jan 1, 2021
 #2
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Hi catmg!

 

So if I'm reading this right:

( y - x ) = 2

( y + x ) = 172

 

- x = 2 - y

x = y - 2

Where did you get y+2?

 

Did I make another addition mistake... I shouldn't stay up late lol

TheOddOne  Jan 1, 2021
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Also, I kept flipping x and z. My fault... It's all supposed to be x so far. The question is what is z?

TheOddOne  Jan 1, 2021
 #4
avatar+112863 
-2

People cannot make sense of it if you cannot get your x's and y's in the right places.

Catmg answered your written question well. 

 

Neither of us know what the question in your head is.... Well I do not anyway.

Melody  Jan 1, 2021
 #5
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Hello TheOddOne again

 

I think I have a better sense of the problem now. 

Consecutive odd number are like 1, 3, and 5 or 7, 9, 11. 

They are odd numbers that are right next to each other. 

Another way to write them is x, x+2, x+4, when x is an odd number. 

If x, y, and z are consecutive odd numbers then y = x + 2 and z = x + 4. 

 

Do you have anymore questions?

I'd love to answer them.

But next time, try to be a bit more careful when writing variables, it can get a bit confusing. 

 

=^._.^=

catmg  Jan 1, 2021
edited by catmg  Jan 1, 2021
 #6
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I don't know how to reedit the question, which I would have if I could. It won't let me.

TheOddOne  Jan 1, 2021
 #7
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Oh, can I ask again in a bit? I think I got it.

TheOddOne  Jan 1, 2021
 #8
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That's amazing. :)))

I love the feeling of finally understanding a problem. 

 

=^._.^=

catmg  Jan 1, 2021
 #9
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Happy new years!

wolfiechan  Jan 1, 2021
 #10
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Dont feel bad everyone makes mistakes!

wolfiechan  Jan 2, 2021
 #11
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Yes,  you can repost it properly if you want.  Make sure you proofread the new question very carefully.

 Jan 2, 2021
edited by Melody  Jan 2, 2021

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