Number Theory

Question

0

446

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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.

Guest Jun 3, 2021

CPhill · Answer 1 · 2021-06-03T08:52:20

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

mworkhard222 · Answer 2 · 2021-06-03T08:58:54

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