document.write( "Question 182230: Find two real numbers that have a sum of 8 and a product of 2. \n" ); document.write( "

Algebra.Com's Answer #136759 by Earlsdon(6294) $\"\"$ $\"About$

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Let x and y be the two numbers, then:
\n" ); document.write( "1) $\"x%2By+=+8\"$ and
\n" ); document.write( "2) $\"x%2Ay+=+2\"$ Rewrite equation 1) as: $\"x+=+8-y\"$ and substitute into equation 2).
\n" ); document.write( "2a) $\"%288-y%29%2Ay+=+8\"$ Simplify.
\n" ); document.write( "2a) $\"8y-y%5E2+=+8\"$ Rewrite this in standard quadratic form.
\n" ); document.write( " $\"y%5E2-8y%2B8+=+0\"$ Solve by the quadratic formula: $\"+y=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"$ where: a = 1, b = -8, and c = 2.
\n" ); document.write( " $\"y+=+%28-%28-8%29%2B-sqrt%28%28-8%29%5E2-4%281%29%282%29%29%29%2F2%281%29\"$ Evaluate.
\n" ); document.write( " $\"y+=+%288%2B-sqrt%2864-8%29%29%2F2\"$
\n" ); document.write( " $\"y+=+%288%2B-sqrt%2856%29%29%2F2\"$
\n" ); document.write( " $\"highlight%28y+=+4%2Bsqrt%2814%29%29\"$ or $\"highlight%28y+=+4-sqrt%2814%29%29\"$ These are the two real numbers.
\n" ); document.write( "Check:
\n" ); document.write( " $\"x%2By+=+8\"$ Substitute $\"x+=+4%2Bsqrt%2814%29\"$ and $\"y+=+4-sqrt%2814%29\"$
\n" ); document.write( " $\"%284%2Bsqrt%2814%29%29%2B%284-sqrt%2814%29%29+=+8%2Bsqrt%2814%29-sqrt%2814%29\"$ = 8
\n" ); document.write( " $\"x%2Ay+=+2\"$ Substitute for x and y as above.
\n" ); document.write( " $\"%284%2Bsqrt%2814%29%29%2A%284-sqrt%2814%29%29+=+16-%28sqrt%2814%29%29%2A%28sqrt%2814%29%29\"$ = $\"16-14+=+2\"$
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