Proving a Simple Inequality with the Given Equality

The 42nd Video
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[@JeremyLionell]

Nice explanation, creative ways to solve them, satisfying animations, and short too. Yet you only have 520 subs?? Well you've got yourself a new One! You deserve it! 🎉

[@user-et5dw8de4i]

let f(x) =1/1+x^4 dψ/dx =- 4x^3/sqr(x^4+1) function decreasing a

[@octobixer]

I set all of them equal to each other to find that individually they all had to be a minimum of 3^0.25 since they're symmetric and the reason it is the minimum is because if you shrink any one of them the other three will increase causing the product to increase as well so the case where the product is at it's smallest is when they are equal

[@sebgor2319]

How to see things like that? Bc it seems to be pulled out of ass for me.

[@user-et5dw8de4i]

Ι apply Lagrange multipliers let F(x,ψ ,z,w) =xψzw min(xψzw) =? G(x,ψ,z,w)=1/x^4+1+1/ψ^4+1+1/z^4+1+1/w^4+1 θF/θχ=λθG/θχ Ψzw=λ4χ^3/sqr(x^4+1) θF/θψ=λθG/θψ χzw=λ4ψ^3/sqr(ψ^4+1) by dividing by members we get x=ψ similar ψ=z z=w therefore 4/x^4+1=1 x^4=3 similar ψ^4=z^4=w^4=3 min(xψzw)=3 That is xψzw.>=3 sqr means second power

[@tajmirisultananupur3841]

First view and first comment... :nice explanation😅