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If 8-x2-y2-2xy=0, for real numbers x and y, what is the value of |x+y|? Express your answer in simplest radical form.

 Jan 14, 2021
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We can solve this algebraically by eliminating the xy  term.....but.....it involves some trigonometry   !!!

 

Easiest to solve this with a graph  :    https://www.desmos.com/calculator/fg6nnvdj6d

 

The graph doesn't explcitly show  it....but......the graph  =  0  when

 

x = -2sqrt (2)   and  y  = 0

x =2sqrt (2)   and y  =  0 

 

So     l  x + y  l  =    l  ± 2sqrt (2)  +  0  l   =    2 sqrt (2)

 

 

cool cool cool

 Jan 14, 2021

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