Is this hard? I think I remember Pythagoras!

Algebra Level 5

∣ 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 + 17 ∣ \left | \sqrt{x^2+4y^2-4xy - 4y + 2x+2} - \sqrt{x^2+4z^2 - 4xz - 4z + 2x+17} \right |

Given that 2 x + y + 3 z = 6 2x+y+3z=6 and x + y + z = 2 x+y+z=2 , find the maximum value of the expression above.

Bonus : Are the values dependent on the variables? Which one?


The answer is 5.

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Abhi Kumbale by Abhi Kumbale , 21, India

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1 solution

Abhi Kumbale
Jan 2, 2016

0 Helpful 0 Interesting 0 Brilliant 0 Confused

We can see that the maximum value is not dependent on values of any variable.

Abhi Kumbale - 5 years, 5 months ago

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.

Bob Kadylo - 4 years, 5 months ago

I think changing the second condition to: x+y+z=2 will make your solution and answer valid.

Bob Kadylo - 4 years, 5 months ago

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Thanks! I've made the corresponding edit.

Calvin Lin Staff - 4 years, 5 months ago

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