System of 3 equations 1 <msqrt> x </msqrt> </mfrac> + 1 <msqrt

Axel York

Axel York

Answered question

2022-06-02

System of 3 equations
1 x + 1 y + z = a 1 y + 1 x + z = b 1 z + 1 x + y = c

Answer & Explanation

Erik Rivera

Erik Rivera

Beginner2022-06-03Added 3 answers

This is an old question, but for the benefit of those who'll come across this and left hanging.
If b = c, then there is an analytic solution which involves an octic that factors into quartics over 2 .
Let x , y , z = p 2 , q 2 , r 2 and, to avoid the octic, let a = 2 a. We get,
1 p + 1 q 2 + r 2 = 2 a 1 q + 1 p 2 + r 2 = b 1 r + 1 p 2 + q 2 = b
and the solution,
p = ( r + 2 a r 2 ) 2 4 a 2 r 2 1 , q = r

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?