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If a + b + c = 9 and ab + bc + ca = 26 find the value of a^2 + b^2 + c^2​.

 Aug 10, 2020
 #1
avatar+1042 
+3

To start this problem, we will first square (a+b+c). This will be, in expanded form, a^2+b^2+c^2+2ab+2ca+2bc=81. Since ab + bc + ca = 26, we can multiply that by two to get 2ab + 2bc + 2ca = 52. Subtract that from our first equation, and we get a^2+b^2+c^2=81-52=29

 

:)

 Aug 10, 2020
 #2
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That was very good.  You just bypassed the individual values of a, b, & c.  That had not occurred to me.  Bravo. 

.

Guest Aug 10, 2020
 #3
avatar+1042 
+2

Thank you, guest :)

ilorty  Aug 12, 2020

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