We have to find all real solutions to this system

Jaylyn Villarreal

Jaylyn Villarreal

Answered question

2022-04-18

We have to find all real solutions to this system of equations:
x=4z21+4z2, y=4x21+4x2, z=4y21+4y2

Answer & Explanation

cadhail6n1t

cadhail6n1t

Beginner2022-04-19Added 14 answers

Let us start solving by taking the first term:
x=4z21+4z2
Assuming z not equal to 0.
xz=4z1+4z2 (1)
Since Arithmetic Mean >= Geometric Mean , we get:
1+4z222z
4z1+4z21 (2)
From (2) and (1), we get
xz1
Similarly for the other two terms we get :
yx1
zy1
This is possible only if: x=y=z

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