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If A2 + B2 = 15 and AB = 10

Forums: Math, Homework, Algebra
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AndyCharles
 
Reply Fri 14 Oct, 2011 05:01 am
If A2 + B2 = 15 and AB = 10, what is the value of the expression
(A – B)2 + (A + B)2 ?

(a) 10.
(b) 20.
(c) 30.
(d) 60.
(e) 70.

Thanks a lot.
Andy Charles
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Type: Question • Score: 1 • Views: 1,251 • Replies: 2
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engineer
 
  2  
Reply Fri 14 Oct, 2011 05:08 am
@AndyCharles,
(a-b)^2 = a^2 - 2ab + b^2
(a+b)^2 = a^2 + 2ab + b^2
-----------------------------------------
= 2 a^2 + 2 b^2

Since a^2 + b^2 = 15, twice that is 30.
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raprap
 
  1  
Reply Fri 14 Oct, 2011 08:52 am
@AndyCharles,
complete the squares and add

hint the ab term cancels

Rap
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