Question Number 9219 by tawakalitu last updated on 23/Nov/16
![Show that: (a + b)[(1/a^2 ) + (1/b^2 )][(a^4 /b^2 ) + (b^4 /a^2 )] ≥ 8(√(ab))](https://www.tinkutara.com/question/Q9219.png)
$$\mathrm{Show}\:\mathrm{that}:\: \\ $$$$\left(\mathrm{a}\:+\:\mathrm{b}\right)\left[\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}} }\right]\left[\frac{\mathrm{a}^{\mathrm{4}} }{\mathrm{b}^{\mathrm{2}} }\:+\:\frac{\mathrm{b}^{\mathrm{4}} }{\mathrm{a}^{\mathrm{2}} }\right]\:\geqslant\:\mathrm{8}\sqrt{\mathrm{ab}} \\ $$
Commented by Yozzias last updated on 23/Nov/16
$$\mathrm{AM}−\mathrm{GM}\:\mathrm{inequality}\:\:\mathrm{a},\mathrm{b}>\mathrm{0} \\ $$