A community for students.
Here's the question you clicked on:
 0 viewing
Ishaan94
 3 years ago
Find all real triples \((x,y, z)\) that satisfy \(x^4+y^4+z^4−4xyz = −1\).
Ishaan94
 3 years ago
Find all real triples \((x,y, z)\) that satisfy \(x^4+y^4+z^4−4xyz = −1\).

This Question is Closed

mahmit2012
 3 years ago
Best ResponseYou've already chosen the best response.0It is just a surface in a 3 dimensional space.

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0I've seen a method to solve problems like this easily, but I can't remember it right now. I'll try and look it up later to try and find more information.

mahmit2012
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1341442265927:dw

mahmit2012
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1341442357328:dw

mahmit2012
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1341442492121:dw

mahmit2012
 3 years ago
Best ResponseYou've already chosen the best response.0So I just found out min(f)=1 so as I told in above that is a surface in a space.

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1hi @Ishaan94 Using Completing the Square \[x^4+y^4+z^44xyz+1=0\\x^42x^2y^2+y^4+2x^2y^2+z^4+2z^22z^24xyz+1=0\\x^42x^2y^2+y^4+2(x^2y^22xyz+z^2)+z^42z^2+1=0\\(x^2y^2)^2+2(xyz)^2+(z^21)^2=0\] so \[x^2y^2=xyz=z^21=0\]

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1only triples that satisfies the equation \[(x,y,z)=(1,1,1),(−1,−1,1),(1,−1,−1),(−1,1,−1)\]

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks @mukushla if it's not too much to ask did you take training or something for the olympiads?

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1welcome my friend no im a chemical engineering student and just love math

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1do u wanna get ready for Math Olympiad or something?

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.0no i am already past my high school but i love solving math problems.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.