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Category:Indian films
Category:2010s Marathi-language filmsQ:

Square root inequality from Gohberg’s book

This is a problem from the book « Abstract Inequalities » of Gohberg

Let $x,y,z$ be nonnegative. Prove that:

If $x^{\frac12},y^{\frac12},z^{\frac12}$ are positives, the solution
is immediate. I need to prove it for the remaining cases.
$(x,y,z)\in\{(0,0,0),(0,1,1),(1,0,1),(1,1,0)\}$ can be proved using AM-GM inequality.
Now, for $(x,y,z)\in\{(0,0,0),(1,0,1)\}$, there exist $a,b,c>0$ such that $x=a^2, y=b^2$ and $z=c^2$. Then

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