∣ ∣ ∣ x 2 + 4 y 2 − 4 x y − 4 y + 2 x + 2 − x 2 + 4 z 2 − 4 x z − 4 z + 2 x + 1 7 ∣ ∣ ∣
Given that 2 x + y + 3 z = 6 and x + y + z = 2 , find the maximum value of the expression above.
Bonus : Are the values dependent on the variables? Which one?
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We can see that the maximum value is not dependent on values of any variable.
I think line 6 in your solution should be -z-y=2 which changes things below that point as well.
2x+y+3z=6 subtract 2x+2y+4z=4 gives 2x-2x+y-2y+3z-4z=6-4 resulting in -z-y=2
This makes line 12 invalid and the whole question needs Revision
See my proposal above.
I think changing the second condition to: x+y+z=2 will make your solution and answer valid.
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