A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
\[\mathsf{a,b,c \in \left[0,1\right]}\]\[\mathsf{\text{Prove}\quad\frac{a}{b+c+1} + \frac{b}{a+c+1} + \frac{c}{a+b+1} + \left(1a\right)\left(1b\right)\left(1c\right)\le1}.\]
 2 years ago
\[\mathsf{a,b,c \in \left[0,1\right]}\]\[\mathsf{\text{Prove}\quad\frac{a}{b+c+1} + \frac{b}{a+c+1} + \frac{c}{a+b+1} + \left(1a\right)\left(1b\right)\left(1c\right)\le1}.\]

This Question is Closed

vishweshshrimali5
 2 years ago
Best ResponseYou've already chosen the best response.1\[\mathsf{\text{Prove}\quad\frac{a}{b+c+1} + \frac{b}{a+c+1} + \frac{c}{a+b+1} + \left(1a\right)\left(1b\right)\left(1c\right)\le1}\] Because \[\mathsf{a,b,c \in \left[0,1\right]}\] It can be easily seen that for a,b,c = 0 or 1 the LHS becomes = 1 Now in all other remaining cases i.e. a,b,c belong to (0,1) each of the fraction will lie in (0,1/3) and each of (1a), (1b),(1c) will lie between (0,1) and so (1a)(1b)(1c) will be approx. = 0 and so the whole LHS < 1 I know that it is a very bad proof But it is just a try. Sorry for this bad attempt

vishweshshrimali5
 2 years ago
Best ResponseYou've already chosen the best response.1(1a)(1b)(1c) will be approx. = 0 this is because product of any three decimals <1 and > 0 their product will be very close to 0

vishweshshrimali5
 2 years ago
Best ResponseYou've already chosen the best response.1@Ishaan94 Can this help u a little ............... ?

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.2another solution using calculus

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0thank you mukushla. i do like the solution, thanks a lot. and thank you vishwesh i had already thought of the way the you did but wasn't able to generate a concrete solution.

vishweshshrimali5
 2 years ago
Best ResponseYou've already chosen the best response.1@mukushla It is really a very nice solution
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.