Find answers of this system of equations in real numbers {x+2/y=3,y+2/z=3, z+2/x=3

Jared Lowe

Jared Lowe

Answered question

2022-11-16

Find answers of this system of equations in real numbers
{ x + 2 y = 3 y + 2 z = 3 z + 2 x = 3

Answer & Explanation

Arely Davila

Arely Davila

Beginner2022-11-17Added 17 answers

We have z = 3 2 x , so
(1) y = 3 2 z = 3 2 3 2 x = 3 2 x 3 x 2 = 7 x 6 3 x 2
Then
0 = x + 2 y 3 = x + 2 ( 3 x 2 ) 7 x 6 3 = 7 x 2 21 x + 14 7 x 6
We deduce 7 x 2 21 x + 14 = 0, i.e. x 2 3 x + 2 = 0, or ( x 1 ) ( x 2 ) = 0, so that x = 1 or x = 2.
In the end we have two solutions: x = y = z = 1 or x = y = z = 2

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