document.write( "Question 732805: The first term of a geometric series are 1,x,y, and the first three terms of an arithmetic series are 1,x,-y. prove that x^2 + 2x -1 = 0. and hence find y, given that x is positive \n" ); document.write( "

Algebra.Com's Answer #448063 by josgarithmetic(39617) $\"\"$ $\"About$

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Geometric sequence must have a common ratio for each successive term.
\n" ); document.write( " $\"x%2F1=y%2Fx\"$
\n" ); document.write( " $\"y=x%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Arithmetic sequence must have a common difference for each successive term.
\n" ); document.write( " $\"x-1=-y-x\"$
\n" ); document.write( " $\"2x-1=-y\"$
\n" ); document.write( " $\"y=-2x%2B1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "There occur two different formulas for y. We equate them:
\n" ); document.write( " $\"x%5E2=-2x%2B1\"$
\n" ); document.write( " $\"x%5E2%2B2x-1=0\"$ That proved!\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Find x through either completing the square or, preferably, use solution to quadratic formula. $\"x=%28-2%2Bsqrt%284-4%2A%28-1%29%29%29%2F2\"$ OR $\"x=%28-2-sqrt%284-4%2A%28-1%29%29%29%2F2\"$ ,
\n" ); document.write( " $\"highlight%28x=-1-sqrt%282%29%29\"$ OR $\"highlight%28x=-1%2Bsqrt%282%29%29\"$ , and you can continue for finding y. \n" ); document.write( "

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