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Hi friends,

 

Please help me with this one:

 

Prove that \(x^2+2xy+2y^2\) cannot be negative for x, y element of R. Thank you all kindly.

 Sep 2, 2020
 #1
avatar+110835 
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I'll give you a good hint juriemagic   

Can you take it from there ?

 

\(x^2+2xy+2y^2\\ =(x^2+2xy+y^2)+y^2\\ =?\)

 

 

 

To be honest, before I even thought about it, I graphed it.  

https://www.desmos.com/calculator/6czdsarjnn

the graph gave me hints and showed me that this expression could not be negative.

 Sep 2, 2020

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