Question

Show that
x dot y = 1/2 ( |x + y^2| - |x|^2 - |y|^2 )

Answer 1

|x+y|²=(x+y)dot(x+y)
=|x|²+xdoty+ydotx+|y|²
=|x|²+2(xdoty)+|y|²
...

Answer 2

i don't get how that proves that |x dot y| equals the right side. can you please continue

Answer 3

|x+y|²=|x|²+2(xdoty)+|y|²
2(xdoty)=|x+y|²-|x|²-|y|²
...