I wonder whether the system of equations and inequations below have a solution. If there are solutio

Mylee Underwood 2022-07-07 Answered
I wonder whether the system of equations and inequations below have a solution. If there are solutions, what are they? A numerical solution is also desired.
{ c 1 1 x 1 + c 2 1 x 2 + c 3 1 x 3 = 0 c 1 1 x 4 + c 2 1 x 5 + c 3 1 x 6 = 0 c 1 ln x 1 1 x 1 + c 2 ln x 2 1 x 2 + c 3 ln x 3 1 x 3 = 0 c 1 ln x 4 1 x 4 + c 2 ln x 5 1 x 5 + c 3 ln x 6 1 x 6 = 0 x 1 ( 1 x 1 ) x 4 ( 1 x 4 ) = x 2 ( 1 x 2 ) x 5 ( 1 x 5 ) = x 3 ( 1 x 3 ) x 6 ( 1 x 6 ) > 1
where c 1 , c 2 , c 3 are constants, and x i ( 0 , 1 ) , i = 1 , 2 , 3 , 4 , 5 , 6
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Answers (1)

haingear8v
Answered 2022-07-08 Author has 13 answers
A simple set of solutions are any ( c 1 , c 2 , c 3 ) such that c 1 + c 2 + c 3 = 0, x 1 = x 2 = x 3 = 1 2 , x 4 = x 5 = x 6 < 1 2

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