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write a system of 3 equations and 3 variables that has the unique solution of (-1,1,2).

 Jul 19, 2020
 #1
avatar+10085 
+2

 

write a system of 3 equations and 3 variables that has the unique solution of (-1,1,2).

 

Hello Guest!

 

\(x+y+z=2\)

\(x y-z=-3\)

\(x+y+z^2=4\)

laugh  !

 Jul 19, 2020
 #2
avatar+10085 
+2

I prove it

 

\(x+y+z=2\\ xy-z=-3\\ x+y+z^2=4 \)

 

\(x=-1\\ y=1\\ z=2\)

 

\(-1+1+2=2\\ -1\cdot 1-2=-3\\ -1+1+2^2=4 \)

q.e.d.

Mistake!
The question asks for a unique solution. The equations are solved by both x = -1, y = 1, z = 2 and x = 1, y = -1, z = 2.
The correction follows.

laugh  !

 Jul 19, 2020
edited by asinus  Jul 19, 2020

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