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How many different triples (a,b,c) from the set {1,2,3,4,5} satisfy the equation a^2 + bc = b^2 + bc?

 Dec 15, 2021
 #1
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All these satisfy your equation. Remove any duplicates:

 

1  = (1, 1, 1)
2  = (2, 2, 1)
3  = (3, 3, 1)
4  = (4, 4, 1)
5  = (5, 5, 1)
6  = (1, 1, 2)
7  = (2, 2, 2)
8  = (3, 3, 2)
9  = (4, 4, 2)
10  = (5, 5, 2)
11  = (1, 1, 3)
12  = (2, 2, 3)
13  = (3, 3, 3)
14  = (4, 4, 3)
15  = (5, 5, 3)
16  = (1, 1, 4)
17  = (2, 2, 4)
18  = (3, 3, 4)
19  = (4, 4, 4)
20  = (5, 5, 4)
21  = (1, 1, 5)
22  = (2, 2, 5)
23  = (3, 3, 5)
24  = (4, 4, 5)
25  = (5, 5, 5)

 Dec 15, 2021
 #2
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+1

How many different triples (a,b,c) from the set {1,2,3,4,5} satisfy the equation a^2 + bc = b^2 + bc

 

a^2 + bc = b^2 + bc

a^2  = b^2 

since there are no negative choices, a=b   c can be any number

 

If numbers cannot be reused then there are no solutions

if numbers can be reused then there are 5*5=25 triplets

 Dec 15, 2021

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