can someone point where is my mistake! (completing the square)

[Gavriell]

 

[MarkFL]

Mind the factor outside the brackets on the expression containing \(y\).

 

[Steven G]

The purple 1 all the way to the right is not correct.

 

[Gavriell]

The purple 1 all the way to the right is not correct.

Thanks! this is my final result, by the way, someone else answered this same problem and their final result is (x-1)²+(z-2)²=2(y-2)²-4 I wonder why he got 2(y-2)² when factoring the y terms.

 

[Steven G]

So which point or points, if any, are on this surface.

 

[Steven G]

Thanks! this is my final result, by the way, someone else answered this same problem and their final result is (x-1)²+(z-2)²=2(y-2)²-4 I wonder why he got 2(y-2)² when factoring the y terms.
View attachment 12807

Bringing that term to other side does NOT negate the fact that you have the sum of three squares equaling -4. There are NO points on this surface! Which point or points, if any would there be if the right hand side constant was 0?

 

[Gavriell]

So which point or points, if any are on this surface.

[MATH](y-2)^2-2\geq0 => (y-2)^2\geq2[/MATH][MATH]|y-2|\geq sqrt(2) [/MATH][MATH]y\geq 2-sqrt(2);-2-sqrt(2) \leq y [/MATH]

 

[Gavriell]

This is my final result.

 

[Steven G]

Bringing that term to other side does NOT negate the fact that you have the sum of three squares equaling -4. There are NO points on this surface! Which point or points, if any would there be if the right hand side constant was 0?

Oops, you did NOT have a SUM of squares which equalled -4. Sorry about that!

 

[lookagain]

This is my final result.View attachment 12808

Gavriell, no, your equation at the bottom of post # 4 should be correct, not what is in the quote box above.
Look at the y terms:

\(\displaystyle -2y^2 + 4y \ \)

\(\displaystyle -2(y^2 - 2y \ + \ ? \ ) \ = \)

\(\displaystyle -2(y^2 - 2y + 1) \ = \ -2(y - 1)^2 \)

 

[Gavriell]

Gavriell, no, your equation at the bottom of post # 4 should be correct, not what is in the quote box above.
Look at the y terms:

\(\displaystyle -2y^2 + 4y \ \)

\(\displaystyle -2(y^2 - 2y \ + \ ? \ ) \ = \)

\(\displaystyle -2(y^2 - 2y + 1) \ = \ -2(y - 1)^2 \)

you are right, this should be the result.