Let-a-b-c-be-positive-real-numbers-with-sum-3-Prove-that-1-a-1-b-1-c-3-2a-2-bc-3-2b-2-ac-3-2c-2-ab-

Question Number 149244 by EDWIN88 last updated on 04/Aug/21

L e t a, b, c b e p o s i t i v e r e a l n u m b e r s

w i t h s u m 3 . P r o v e t h a t

\frac{1}{a} + \frac{1}{b} + \frac{1}{c} ⩾ \frac{3}{2 a^{2} + b c} + \frac{3}{2 b^{2} + a c} + \frac{3}{2 c^{2} + a b}