Question

VREAU EX A6
PLSSSS AM NEVOIE URGENTA DE EL!!!!!!
VA ROGGG
DAU 50 DE PUNCTE​

Answer 1

Explicație pas cu pas:

a, b, c sunt numere reale pozitive

$(ab + bc + ca)\Big|1 - \dfrac{1}{abc} \Big| =$

$= ab\Big|1 - \dfrac{1}{abc} \Big| + bc\Big|1 - \dfrac{1}{abc} \Big| + ca \Big|1 - \dfrac{1}{abc} \Big| \leqslant$

$\leqslant \Big|ab\Big(1 - \dfrac{1}{abc} \Big)\Big| + \Big|bc\Big(1 - \dfrac{1}{abc} \Big)\Big| + \Big|ca\Big(1 - \dfrac{1}{abc} \Big)\Big|$

$= \Big|ab - \dfrac{ab}{abc}\Big| + \Big|bc - \dfrac{bc}{abc} \Big| + \Big|ca - \dfrac{ca}{abc}\Big|$

$= \Big|ab - \dfrac{1}{c}\Big| + \Big|bc - \dfrac{1}{a} \Big| + \Big|ca - \dfrac{1}{b}\Big|$

q.e.d.