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


    $\sqrt{a(1-b)(1-c)}+ \sqrt{b(1-a)(1-c)}+\sqrt{c(1-a)(1-b)} \le 1 + \sqrt{abc}$
    Last edited by lfdahl; March 3rd, 2017 at 12:59. Reason: Correction of typo, thanks to Albert!

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

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    #3 Thread Author
    Youre right, Albert. Ive made a typo. The inequality sign should be reversed. Im sorry for my mistake.

    Thankyou for pointing this out to me.

    Cheers, lfdahl

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    Quote Originally Posted by lfdahl View Post
    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:
    Last edited by Albert; March 6th, 2017 at 09:26.

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    Very nice solution, Albert!

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