document.write( "Question 519299: if a,b,c,d are in continued proportion, prove that (a+b)(b+c)-(a+c)(b+d)=(b-c)^2 \n" ); document.write( "

Algebra.Com's Answer #345522 by Edwin McCravy(20060) $\"\"$ $\"About$

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if a,b,c,d are in continued proportion, prove that \r
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document.write( "Sorry, but that isn't true, for here is a counter-example:\r\n" );
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document.write( "For a,b,c,and d to be in continued proportion,\r\n" );
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document.write( "a:b = b:c  =  c:d\r\n" );
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document.write( "3:9 = 9:27 = 27:81 \r\n" );
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document.write( "Let a=3, b=9, c=27, d=81\r\n" );
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document.write( "   (a+b)(b+c)-(a+c)(b+d)≟(b-c)²\r\n" );
document.write( "(3+9)(9+27)-(3+27)(9+81)≟(9-27)²\r\n" );
document.write( "       (12)(36)-(30)(90)≟(-18)²\r\n" );
document.write( "            432 - 2700  ≟ 324\r\n" );
document.write( "                 -2268  ≠ 324\r\n" );
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document.write( "Edwin

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