document.write( "Question 1179366: Let x, a, b, c be nonnegative real numbers. Prove that
\n" ); document.write( "(x + cuberoot{abc})^3 <= (x + a)(x + b)(x + c) <= ( x + {(a+b+c)/(3)}^3) \n" ); document.write( "

Algebra.Com's Answer #808933 by math_helper(2461) $\"\"$ $\"About$

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document.write( "See this:
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document.write( "https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means\r
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document.write( "and\r
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document.write( "https://math.stackexchange.com/questions/1298115/prove-inequality-abbcca-ge-3-abc-1\r
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document.write( "If you expand the left hand side you will get:\r
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document.write( "     = \r
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document.write( "Expanding the middle gives:
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document.write( "     = \r
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document.write( "Comparing term-by term, you get two inequalities to prove:
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document.write( "     \r
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document.write( "The LHS is a GM, the RHS is an AM,  so here the AM-GM inequality applies.\r
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document.write( "The middle term compared to the RHS (in original problem statement) is then proven in a similar fashion.\r
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