document.write( "Question 1077333: Find all pairs of real numbers (x,y) such that x + y = 6 and x^2 + y^2 = 28. If you find more than one pair, then list your pairs in order by increasing x value, separated by commas. \n" ); document.write( "

Algebra.Com's Answer #691823 by MathLover1(20849) $\"\"$ $\"About$

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all pairs of real numbers ( $\"x\"$ , $\"y\"$ ) such that $\"+x+%2B+y+=+6\"$ and $\"x%5E2+%2B+y%5E2+=+28\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+%2B+y+=+6+\"$ ...solve for $\"x\"$
\n" ); document.write( " $\"x+=+6+-y\"$ \r
\n" ); document.write( "\n" ); document.write( "substitute in $\"x%5E2+%2B+y%5E2+=+28\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%286-y%29%5E2+%2B+y%5E2+=+28\"$ .....solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36-12y%2By%5E2+%2B+y%5E2+=+28\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"36-12y%2B2y%5E2++-28=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2y%5E2-12y%2B36++-28=0\"$ ....both sides divide by $\"2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y%5E2-6y%2B18++-14=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y%5E2-6y%2B4=0\"$ .......complete square\r
\n" ); document.write( "\n" ); document.write( " $\"%28y%5E2-6y%2Bb%5E2%29-b%5E2%2B4=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28y%5E2-6y%2B3%5E2%29-3%5E2%2B4=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28y-3%29%5E2-9%2B4=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28y+-+3%29%5E2+-+5+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28y+-+3%29%5E2+=+5+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28y+-+3%29+=+sqrt%285+%29\"$ \r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( " $\"y=3%2Bsqrt%285+%29\"$ or $\"y=3-sqrt%285+%29+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now find $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+6+-y\"$ => $\"x+=+6+-%283%2Bsqrt%285+%29%29=6-3-sqrt%285+%29\"$ => $\"x=3-sqrt%285+%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"x+=+6+-y\"$ => $\"x+=+6+-%283-sqrt%285+%29%29=6-3%2Bsqrt%285+%29\"$ => $\"x=3%2Bsqrt%285+%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so, ( $\"x\"$ , $\"y\"$ ) pairs are:\r
\n" ); document.write( "\n" ); document.write( "( $\"3%2Bsqrt%285+%29\"$ , $\"3-sqrt%285+%29\"$ )\r
\n" ); document.write( "\n" ); document.write( "and\r
\n" ); document.write( "\n" ); document.write( "( $\"3-sqrt%285+%29\"$ , $\"3%2Bsqrt%285+%29\"$ )
\n" ); document.write( " \n" ); document.write( "

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