Solve the system of equations:

\(\sqrt x + \sqrt y + \sqrt z + 1 = 4\sqrt{xyz}\\ xy + yz + zx + 3 = 2\cdot \left(\sqrt[4]{x} +\sqrt[4]{y}+\sqrt[4]{z}\right)\)

MaxWong
Feb 15, 2017

#1**0 **

Hello Max: This is the huge "mess" I got when I plugged into Wolfram/Alpha!!!.

http://www.wolframalpha.com/input/?i=(x)%2B(y)%2B(z)%2B1%3D16(xyz),+(xy)%5E4%2B(yz)%5E4%2B(xz)%5E4%2B81%3D16*%5B(x)%2B(y)%2B(z)%5D,+solve+for+x,y,z

Guest Feb 15, 2017

#3**0 **

Any full solutions? I don't need you to look up on Wolfram Alpha and tell me the answer is x = y = z = 1....... I can do that too......

Sorry for being impolite.

MaxWong
Feb 17, 2017

#4**+5 **

Hi, I'm guest #2 (different from guest #1).

I did not use Wolfram Alpha, I just looked at the equations and wrote down the blindingly obvious solution.

There might be other solutions, but frankly I have better things to do with my time than to look for them, (if they exist that is).

Don't apologise for being impolite, just don't be impolite.

Guest Feb 17, 2017