
MHB Journeyman
#1
March 2nd, 2017,
15:57
Let $0 \le a,b,c \le 1.$ Prove the inequality:
$\sqrt{a(1b)(1c)}+ \sqrt{b(1a)(1c)}+\sqrt{c(1a)(1b)} \le 1 + \sqrt{abc}$
Last edited by lfdahl; March 3rd, 2017 at 12:59.
Reason:
Correction of typo, thanks to Albert!

March 2nd, 2017 15:57
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MHB Master
#2
March 3rd, 2017,
05:36
Originally Posted by
lfdahl
Let $0 \le a,b,c \le 1.$ Prove the inequality:$\sqrt{a(1b)(1c)}+ \sqrt{b(1a)(1c)}+\sqrt{c(1a)(1b)} \ge 1 + \sqrt{abc}(1)$

MHB Journeyman
#3
March 3rd, 2017,
12:57
Thread Author
Originally Posted by
Albert
You´re right, Albert. I´ve made a typo. The inequality sign should be reversed. I´m sorry for my mistake.
Thankyou for pointing this out to me.
Cheers, lfdahl

MHB Master
#4
March 6th, 2017,
03:29
Originally Posted by
lfdahl
Let $0 \le a,b,c \le 1.$ Prove the inequality:
$\sqrt{a(1b)(1c)}+ \sqrt{b(1a)(1c)}+\sqrt{c(1a)(1b)} \le 1 + \sqrt{abc}$
my solution:
Last edited by Albert; March 6th, 2017 at 09:26.

MHB Journeyman
#5
March 6th, 2017,
11:01
Thread Author
Originally Posted by
Albert
Very nice solution, Albert!