+73 Three consecutive positive odd integers $a,b$ and $c$ satisfy $b^{2}-a^{2}=344$ and $c^{2}-b^{2}>0.$ What is the value of $c^{2}-b{^2}$?
+9466 b2 - a2 > 0 so b2 > a2 and so since a, b are positive, b > a
c2 - b2 > 0 so c2 > b2 and so since c, b are positive, c > b
So a < b < c
And since a, b, and c are consecutive positive odd integers:
b = a + 2
c = a + 4
Now we can find a using this equation:
b2 - a2 = 344
(a + 2)2 - a2 = 344
(a + 2)(a + 2) - a2 = 344
a2 + 4a + 4 - a2 = 344
4a + 4 = 344
4a = 340
a = 85
Since a = 85, b = 87 and c = 89
And so c2 - b2 = 892 - 872 = 352
+73 Thanks hectictar! Also, happy $21$st and $22$nd birthday (sorry I couldn't say this at your real birthday I joined two weeks ago).
+73 The answer was correct and the exact explanation for how to solve after I put in $352$ was almost exactly what you said! Thank you a million!
