document.write( "Question 482149: Pls Help me with this question urgently,thanks. Find the three numbers in a geometric progression whose sum is 28 and whose product is 512. \n" ); document.write( "

Algebra.Com's Answer #330120 by Edwin McCravy(20056) $\"\"$ $\"About$

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. Find the three numbers in a geometric progression whose sum is 28 and whose product is 512.\r
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document.write( "Let a = the first number\r\n" );
document.write( "Let r = the common ratio of the geometric progression\r\n" );
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document.write( "Then ar = 2nd number\r\n" );
document.write( "and  ar² = 3rd number\r\n" );
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document.write( ">>...sum is 28...<<\r\n" );
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document.write( "a + ar + ar² = 28\r\n" );
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document.write( "a(1 + r + r²) = 28\r\n" );
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document.write( ">>...product is 512...<<\r\n" );
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document.write( "(a)(ar)(ar²) = 512\r\n" );
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document.write( "        a³r³ = 512\r\n" );
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document.write( "Take cube roots of both sides\r\n" );
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document.write( "          ar = ∛512\r\n" );
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document.write( "          ar = 8\r\n" );
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document.write( "           a =  \r\n" );
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document.write( "Substitute in             \r\n" );
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document.write( "a(1 + r + r²) = 28\r\n" );
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document.write( "(1 + r + r²) = 28\r\n" );
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document.write( "Multiply both sides by r\r\n" );
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document.write( "        8(1 + r + r²) = 28r\r\n" );
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document.write( "Divide both sides by 4\r\n" );
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document.write( "        2(1 + r + r²) = 7r\r\n" );
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document.write( "         2 + 2r + 2r² = 7r\r\n" );
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document.write( "         2r² - 5r + 2 = 0\r\n" );
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document.write( "Factor the left side:\r\n" );
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document.write( "      (2r - 1)(r - 2) = 0\r\n" );
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document.write( "  2r - 1 = 0       r - 2 = 0  \r\n" );
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document.write( "      2r = 1           r = 2\r\n" );
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document.write( "       r = \r\n" );
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document.write( "So we have two solutions for r\r\n" );
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document.write( "Using r = \r\n" );
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document.write( "           a =  \r\n" );
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document.write( "           a = \r\n" );
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document.write( "           a =  \r\n" );
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document.write( "           a = 16\r\n" );
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document.write( "So one solution is these three numbers using a = 16 and r = :\r\n" );
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document.write( "a, ar, ar² or 16, 8, 4\r\n" );
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document.write( "Using r = 2\r\n" );
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document.write( "           a =  \r\n" );
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document.write( "           a = \r\n" );
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document.write( "           a = 4\r\n" );
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document.write( "So one solution is these three numbers using a = 4 and r = 2:\r\n" );
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document.write( "a, ar, ar² or 4, 8, 16\r\n" );
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document.write( "Solutions: 16,8,4  or 4,8,16\r\n" );
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document.write( "Edwin

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