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x,y,z are three consecutive positive odd integers that satisfy y^2 - x^2 = 384. Find the value of z.

 
 Jun 3, 2021
 #1
avatar+119772 
+1

Let     y  =   n      x =  n - 2      and z = n + 2

 

So

 

n^2   -  ( n - 2)^2  =  384

 

n^2  - n^2  + 4n   -  4   =  384

 

4n  =  384 + 4

 

4n =  388

 

n  =  388/  4    =    97

 

So

 

z =  n + 2   = 99

 

cool cool cool

 
 Jun 3, 2021
 #2
avatar+369 
+2

well, y must be greater than x, so x + 2 = y.

 

\(y^2-x^2=384\) and \(x + 2 = y\)

 

so solving that system of equations... u get \(x=95, \: y=97\)

 

so 97 + 2 = 99

 
 Jun 3, 2021

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