document.write( "Question 1188523: Find the product(xy) if $\"+x%2By%2B+sqrt%28+x%2By+%29+=+20+\"$ and $\"+x-y%2B+sqrt%28+x-y+%29+=+12+\"$ \n" ); document.write( "

Algebra.Com's Answer #819632 by ikleyn(52779) $\"\"$ $\"About$

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\n" ); document.write( "Find the product(xy) if $\"+x%2By%2B+sqrt%28+x%2By+%29+=+20+\"$ and $\"+x-y%2B+sqrt%28+x-y+%29+=+12+\"$
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document.write( "Let   = p.     (1)\r\n" );
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document.write( "Then first equation takes the form\r\n" );
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document.write( "    p^2 + p - 20 = 0,  or, factoring,  (p+5)*(p-4) = 0.     (2)\r\n" );
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document.write( "Its roots are p= -5 and p= 4.\r\n" );
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document.write( "Due to definition of p  (1), we suppose, by default, that \"p\" is positive; so we choose p= 4.\r\n" );
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document.write( "Hence,  x + y = 4^2 = 16.     (3)\r\n" );
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document.write( "Let   = q.     (4)\r\n" );
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document.write( "Then second equation takes the form\r\n" );
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document.write( "    q^2 + q - 12 = 0,  or, factoring,  (q+4)*(q-3) = 0.     (5)\r\n" );
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document.write( "Its roots are q= -4 and q= 3.\r\n" );
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document.write( "Due to definition of q  (4), we suppose, by default, that \"q\" is positive; so we choose q= 3.\r\n" );
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document.write( "Hence,  x - y = 3^2 = 9.     (6)\r\n" );
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document.write( "Thus we have these two equations\r\n" );
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document.write( "    x + y = 16     (3)\r\n" );
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document.write( "    x - y =  9     (6)\r\n" );
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document.write( "Solving by elimination, we get  x =  =  = 12.5;  y = 16-x = 16-12.5 = 3.5.\r\n" );
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document.write( "THEREFORE,  x*y = 12.5*3.5 = 43.75.      ANSWER\r\n" );
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