document.write( "Question 1119640: Three numbers are in the ratio of 1:5:9. If the second number is diminished by 8, the three numbers will form a geometric sequence. What are the three numbers? \n" ); document.write( "

Algebra.Com's Answer #735245 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "The problem has 2 (two) solutions/answers.\r
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\n" ); document.write( "\n" ); document.write( "One answer (as found by John) for three numbers is 4, 20, 36.\r
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\n" ); document.write( "\n" ); document.write( "The other answer for three numbers is 1, 5, 9.\r
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\n" ); document.write( "\n" ); document.write( "Solution\r
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document.write( "From the condition, the three numbers are x, 5x and 9x.\r\n" );
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document.write( "The condition that three numbers x, (5x-8) and 9x form a geometric progression is this equality (equation)\r\n" );
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document.write( " = ,     (1)\r\n" );
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document.write( "saying that the ratio of the third to the second term of the GP is the same as the ratio of the second to the first.\r\n" );
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document.write( "From (1), \r\n" );
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document.write( "9x^2 = (5x-8)^2,\r\n" );
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document.write( "9x^2 = 25x^2 - 80x + 64,\r\n" );
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document.write( "16x^2 - 80x + 64 = 0\r\n" );
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document.write( "with the roots   = 4,    = 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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