# Thread: Inequality - proof wanted

1. Let $0 \le a,b,c \le 1.$ Prove the inequality:

$\sqrt{a(1-b)(1-c)}+ \sqrt{b(1-a)(1-c)}+\sqrt{c(1-a)(1-b)} \le 1 + \sqrt{abc}$

2.

3. Originally Posted by lfdahl
Let $0 \le a,b,c \le 1.$ Prove the inequality:$\sqrt{a(1-b)(1-c)}+ \sqrt{b(1-a)(1-c)}+\sqrt{c(1-a)(1-b)} \ge 1 + \sqrt{abc}(1)$

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

5. Originally Posted by lfdahl
Let $0 \le a,b,c \le 1.$ Prove the inequality:

$\sqrt{a(1-b)(1-c)}+ \sqrt{b(1-a)(1-c)}+\sqrt{c(1-a)(1-b)} \le 1 + \sqrt{abc}$
my solution: