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Inequality

We have a,b,c>0. Prove (a+b/ac)(b+c/ab)(c+a/bc)>=8 Please help me. Thanks.

Note by Hermione Taylor
3 years, 7 months ago

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Using AM-GM inequality, a+(b/ac)>2(b/c) , b+(c/ab)>2c/a , c+(a/bc)>2a/b, Multiplying these expressions you would automatically get the result. Siddharth Kumar · 3 years, 7 months ago

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@Siddharth Kumar You're wrong, but the principle is right. \(a+\frac{b}{ac} \geq 2\sqrt{\frac{b}{c}}\). You just forgot the square root. But when you multiply them together, they cancel anyways, leaving a 1 under the square root. Bob Krueger · 3 years, 7 months ago

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@Bob Krueger Actually I entered the square root but it was not displayed in the answer, don't know why. Siddharth Kumar · 3 years, 7 months ago

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@Siddharth Kumar Weird. Oh well. It works anyways. Bob Krueger · 3 years, 7 months ago

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@Siddharth Kumar Get it. Thank you very much Hermione Taylor · 3 years, 7 months ago

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help me plz we have ab+bc+ca=0 calculate (a+b/c)+(b+c/a)+(c+a/b) Khaoula Ghayati · 2 years, 2 months ago

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