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Three consecutive positive odd integers a,b and c satisfy b^{2}-a^{2}=\(48\) and c^{2}-b^{2}>0. What is the value of c^{2}-b{^2}?

 Apr 29, 2022
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Let a =  2n+ 1   and b  = 2n + 3

 

So

 

(2n + 3)^2  - (2n + 1)^2  = 48

 

4n^2  + 12n + 9  -  4n^2  - 4n - 1  = 48

 

8n  +  8  =  48       divide through by 8

 

n + 1  =   6

 

n =  5

 

So

 

a =  11      b =  13      c  = 15

 

And

 

c^2  -  b^2   =

 

15^2 -  13^2   =  56

 

 

cool cool cool

 Apr 29, 2022

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