AM-GM Inequality

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Student 999
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#1
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#1
Could someone hint to me another approach or how I would go about using my method to get an answerName:  IMG_FA4EBD8B394C-1.jpeg
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I think the issue with my attempt is that part I considered the am-gm of xy+zt since the inequality sign of xy+zt>= 4 doesn't work in subbing into my original inequality as you something like xy+zt<= (number) to get an answer?Name:  Screenshot 2022-06-28 at 15.43.05.png
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Last edited by Student 999; 1 month ago
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HardlyHuman
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#2
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Spoiler:
Show
use GM-AM on (x +y)(z + t)

Spoiler:
Show
use GM-AM on 2(xy + zt)

some hints, hopefully should be useful
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Student 999
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#3
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(Original post by HardlyHuman)
Spoiler:
Show
use GM-AM on (x +y)(z + t)

Spoiler:
Show
use GM-AM on 2(xy + zt)

some hints, hopefully should be useful
Not quite sure what you mean isn't that what I've done above, could you write out the first line?
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mqb2766
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#4
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One thing, in addition to the previous hints, is when a problem has this many variables, its a good to make sure you understand what happens on a simplified problem. So could you solve
max x+y
x^2+y^2 = 5
xy = 2
The relationship to the original problem should be clear? However, it gives an idea (you can plot them in desmos) of the role of the constraints and the set of feasible (x,y) values to maximize.

Edit if you can show the function is <= 9 and that you can find a solution where its equal to that value, then that must be the max.
Last edited by mqb2766; 1 month ago
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