Is it possible to write this equation explicitly in terms of y?
xy/2 = x + y + (x^2+y^2)^(1/2)

Question

Is it possible to write this equation explicitly in terms of y? 
xy/2 = x + y + (x^2+y^2)^(1/2)

amistre64 · Answer

maybe the wolf can help out with that ...

amistre64 · Answer

its looks possible http://www.wolframalpha.com/input/?i=xy%2F2+%3D+x+%2B+y+%2B+%28x%5E2%2By%5E2%29%5E%281%2F2%29

danmac0710 · Answer

Who or what is the wolf??

danmac0710 · Answer

Wolfram Alpha!! Of course! Wow does it do that kind of thing? Impressive!

asnaseer · Answer

you should be able to do this quite simply by isolating the (x^2+y^2)^(1/2) on one-side of the equation and then squaring both sides.

asnaseer · Answer

$$\frac{xy}{2}=x+y+\sqrt{x^2+y^2}$$now multiply both sides by 2 to get:$$xy=2x+2x+2\sqrt{x^2+y^2}$$re-arrange to get:$$2\sqrt{x^2+y^2}=xy-2x-2y$$square both sides:$$4(x^2+y^2)=(xy-2x-2y)^2=x^2y^2-4x^2y+4x^2-4xy^2+8xy+4y^2$$the 4x^2 and 4y^2 appear on both sides of the equation and so can be cancelled out, leaving:$$0=x^2y^2-4x^2y-4xy^2+8xy$$you should be able to solve from here...