An algebra problem by Akash Pachauri
Algebra
Level
3
Find minimum value of [(x)^6+(y)^6+2(z)^3+2(w)^3]/[wxyz]. Where, w,x,y,z>0
The answer is 6.
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1 solution
as, arithmetic mean> geometric mean So, (x^6+y^6+z^3+z^3+w^3+w^3)/6 >[(x^6)(y^6)(z^6)(w^6)]^(1/6) (x^6+y^6+z^3+z^3+w^3+w^3)/(wxyz)>6