Solve two equations for a and b { <mtable columnalign="left left" rowspa

seupeljewj

seupeljewj

Answered question

2022-06-16

Solve two equations for a and b
{ c 2 = c 1 a ( ( c 3 b ) 3 1 ) b 2 = a 2 + c 3 2 + 2 ( a ) ( c 3 ) ( c 4 )

Answer & Explanation

rioolpijpgp

rioolpijpgp

Beginner2022-06-17Added 19 answers

The system
{ c 2 = c 1 a ( ( c 3 b ) 3 1 ) b 2 = a 2 + c 3 2 + 2 a c 3 c 4
is equivalent to
{ a = c 1 c 3 3 x 3 c 2 x 3 b = x ,
where x is a solution of the following septic equation I've obtained in SWP:
0 = c 2 2 x 7 + c 3 c 2 2 x 6 + ( c 1 2 + 2 c 1 c 3 c 4 c 2 ) x 5 + ( 2 c 3 2 c 1 c 4 c 2 c 3 c 1 2 ) x 4 + ( 2 c 3 3 c 1 c 4 c 2 c 1 2 c 3 2 ) x 3 + c 1 2 c 3 3 x 2 + c 1 2 c 3 4 x + c 1 2 c 3 5 .
The general septic equation cannot be solved algebraically.
Note: In the present form of the system a should be different from 0. So b = c 3 , a = 0 is no longer a solution.

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