+0  
 
+2
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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 + ac ?

 

Work: 

 

a^2 + bc = b^2 + ac 

0 = b^2 + s^2 + ac + bc

2ba = c(b+a) + (b^2 + 2ba + a^2)

2ba = (b+a) (b+a) + c (a+b)

2ba = (b+a+c) (b+a)

 

How do I go from here?

 Dec 29, 2020

Best Answer 

 #1
avatar+31512 
+4

a^2 + bc = b^2 + ac

Rearrange as a^2 - b^2 = ac - bc

Factor as (a+b)(a-b) = (a-b)c

Simplify, a + b = c

Can you take it from here?

 Dec 29, 2020
 #1
avatar+31512 
+4
Best Answer

a^2 + bc = b^2 + ac

Rearrange as a^2 - b^2 = ac - bc

Factor as (a+b)(a-b) = (a-b)c

Simplify, a + b = c

Can you take it from here?

Alan Dec 29, 2020
 #2
avatar+28 
+1

Ah, yeah! Thank you so much! :D

TheOddOne  Jan 1, 2021

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