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!)

TheOddOne Jan 1, 2021

#1**+1 **

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. :)))

=^._.^=

catmg Jan 1, 2021

#2**0 **

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

#3**0 **

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**-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**0 **

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

#6**0 **

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