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.
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)