document.write( "Question 973163: if arithmetic mean and geometric mean are inserted between a and b, such that arithmetic mean is double the geometric mean . show that ratio of a and b is [2+(3)^(1/2)]/[2-(3)^(1/2)] \n" ); document.write( "

Algebra.Com's Answer #595598 by Edwin McCravy(20056) $\"\"$ $\"About$

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If an arithmetic mean and a geometric mean are inserted between a and b, such
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document.write( "We change the  powers to square roots\r\n" );
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document.write( "Then we rationalize the denominator:\r\n" );
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\n" ); document.write( ">>...the arithmetic mean is double the geometric mean...<<
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document.write( "Multiply both sides by 2 to clear the fraction:\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "Solve for \"a\" using the quadratic formula.  We will use capital\r\n" );
document.write( "letters in the quadratic formula to avoid conflict of notation:\r\n" );
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document.write( "where , , \r\n" );
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document.write( "Divide both sides by b\r\n" );
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document.write( "We have shown that the ratio is either  or .\r\n" );
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document.write( "So you might point out to your teacher that the problem as it is stated here,\r\n" );
document.write( "is not necessarily true.\r\n" );
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document.write( "The problem should be stated this way:\r\n" );
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\n" ); document.write( "If an arithmetic mean and a geometric mean are inserted between a and b, such
\n" ); document.write( "that the arithmetic mean is double the geometric mean. show that ratio of a and
\n" ); document.write( "b is [2+(3)^(1/2)]/[2-(3)^(1/2)] OR [2-(3)^(1/2)]/[2+(3)^(1/2)].
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document.write( "The second one, when the  powers are changed to square roots and its\r\n" );
document.write( "denominator is rationalized, becomes .\r\n" );
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document.write( "Edwin

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