document.write( "Question 773286: find three numbers in geometric progression whose sum is 19 and product is 216. \n" ); document.write( "

Algebra.Com's Answer #471403 by ramkikk66(644) $\"\"$ $\"About$

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document.write( "find three numbers in geometric progression whose sum is 19 and product is 216.\r\n" );
document.write( "Ans:\r\n" );
document.write( "Let the middle term be x and the common ratio be r. Then the 1st and 3rd terms are\r\n" );
document.write( "x/r and x*r respectively.\r\n" );
document.write( "Product = (x/r)*x*r*x = x^3 = 216.\r\n" );
document.write( "So middle term x = 6.\r\n" );
document.write( "Then the sum of the 3 terms = 6/r + 6 + 6*r = 19.\r\n" );
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document.write( "Multiplying by r\r\n" );
document.write( " This is a standard quadratic equation which can be\r\n" );
document.write( "solved using the quadratic solver, as shown below.\r\n" );
document.write( "The 2 roots are r = 2/3 and r = 3/2.\r\n" );
document.write( "Hence the other 2 terms of the GP are (6*2/3) and (6/(2/3) = 4 and 9.\r\n" );
document.write( "The 3 numbers are 4,6 and 9 (or 9,6 and 4).\r\n" );
document.write( "Hope you got it :)\r\n" );
document.write( "Solution using quadratic solver: \n" );
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document.write( "Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:\r\n" );
document.write( "  \r\n" );
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document.write( "  \r\n" );
document.write( "  For these solutions to exist, the discriminant  should not be a negative number.\r\n" );
document.write( "  \r\n" );
document.write( "  First, we need to compute the discriminant : .\r\n" );
document.write( "  \r\n" );
document.write( "  Discriminant d=25 is greater than zero. That means that there are two solutions: .\r\n" );
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document.write( "    Quadratic expression  can be factored:\r\n" );
document.write( "  \r\n" );
document.write( "  Again, the answer is: 1.5, 0.666666666666667.\n" );
document.write( "Here's your graph:\n" );
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