document.write( "Question 975018: Insert 2 arithmetic means between x+y and 4x-2y
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Algebra.Com's Answer #597218 by Edwin McCravy(20056) $\"\"$ $\"About$

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Insert 2 arithmetic means between x+y and 4x-2y
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document.write( "Let the two arithmetic means be A and B, and the common difference be d.\r\n" );
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document.write( "Then the arithmetic sequence with 4 ternms goes:\r\n" );
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document.write( "x+y, A, B, 4x-2y\r\n" );
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document.write( "where\r\n" );
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document.write( "A = x+y+d\r\n" );
document.write( "B = x+y+2d\r\n" );
document.write( "B+d = 4x-2y\r\n" );
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document.write( "Substituting for B\r\n" );
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document.write( "x+y+2d+d = 4x-2y\r\n" );
document.write( "x+y+3d = 4x-2y\r\n" );
document.write( "    3d = 3x-3y\r\n" );
document.write( "     d = x-y\r\n" );
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document.write( "A = x+y+d = x+y+x-y = 2x\r\n" );
document.write( "B = x+y+2d = x+y+2(x-y) = x+y+2x-2y = 3x-y\r\n" );
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document.write( "x+y, 2x, 3x-y, 4x-2y\r\n" );
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document.write( "The two arithmetic means are 2x and 3x-y\r\n" );
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document.write( "Edwin

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