Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 151142 by mathdanisur last updated on 18/Aug/21

if  x;y;z∈R^+   and  (1/x^2 ) + (1/y^2 ) + (1/z^2 ) = ((27)/4)  prove that:  ((x^3  + y^2 )/(x^2  + y^2 )) + ((y^3  + z^2 )/(y^2  + z^2 )) + ((z^3  + x^2 )/(z^2  + x^2 )) ≥ (5/2)

$$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\in\mathbb{R}^{+} \:\:\mathrm{and}\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{2}} }\:=\:\frac{\mathrm{27}}{\mathrm{4}} \\ $$$$\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }\:+\:\frac{\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{2}} }{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} }\:+\:\frac{\mathrm{z}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{2}} }{\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{2}} }\:\geqslant\:\frac{\mathrm{5}}{\mathrm{2}} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com