document.write( "Question 407134: Two positive real numbers have a sum of 7 and a product of 11. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #287045 by richard1234(7193) $\"\"$ $\"About$

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Suppose that x and y are the numbers, such that x + y = 7 and xy = 11. Two ways to solve this:\r
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\n" ); document.write( "\n" ); document.write( "Solution 1:
\n" ); document.write( "Substitute y = 7 - x into the second equation to obtain x(7 - x) = 11. Now you can find x using the quadratic formula.\r
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\n" ); document.write( "\n" ); document.write( "Solution 2: Assume that x and y are roots of a polynomial of the form $\"z%5E2+%2B+bz+%2B+c\"$ . Applying Viete's formulas, the sum of the roots of the polynomial is -b, and the product is c, so we have\r
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\n" ); document.write( "\n" ); document.write( " $\"z%5E2+-+7z+%2B+11+=+0\"$ . The roots of z are the values of x and y. Note that this is the same quadratic as in the previous solution. \n" ); document.write( "

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