document.write( "Question 888262: Numbers a, b and c are such that a ≥ 0, b ≥ 0 and c ≥ 0. Prove:
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Algebra.Com's Answer #537274 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

To prove:\r\n" );
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document.write( "By Cauchy's inequality, the arithmetic mean of any number of \r\n" );
document.write( "positive numbers is greater than or equal to the geometric mean.\r\n" );
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document.write( "Let's take two of the cubes to be the same.\r\n" );
document.write( "The arithmetic mean of ,, and  is greater\r\n" );
document.write( "than or equal to the geometric mean of those cubes, two of which are the same.\r\n" );
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document.write( "By symmetry we can also prove that\r\n" );
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document.write( "Add all 6 inequalities:\r\n" );
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document.write( "Divide through by 3\r\n" );
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document.write( "Factor out 2 on the left.\r\n" );
document.write( "Rearrange the terms on the right so we can factor \r\n" );
document.write( "pairwise and get the given desired right side: \r\n" );
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document.write( "On the right, factor the 1st two, middle two and last two terms:\r\n" );
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document.write( "Edwin

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