document.write( "Question 1104242: Find the product (xy) if x+y+ $\"+sqrt%28+x%2By+%29+\"$ = 20 and x-y+ $\"sqrt+%28+x-y+%29+\"$ =12. \n" ); document.write( "

Algebra.Com's Answer #718992 by ikleyn(52814) $\"\"$ $\"About$

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document.write( "It is assumed in the given equations  that   >= 0  and   >= 0.\r\n" );
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document.write( "1.  Let u = .  Then\r\n" );
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document.write( "     = 20,   or\r\n" );
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document.write( "     = 0.\r\n" );
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document.write( "    Factor left side\r\n" );
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document.write( "    (u+5)*(u-4) = 0.\r\n" );
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document.write( "    As  just noticed above,  assumed to be >= 0.\r\n" );
document.write( "    Therefore, only positive root  u = 4  works.\r\n" );
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document.write( "    Thus,   = 4.   Then  x + y = 4^2 = 16.\r\n" );
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document.write( "2.  Similarly, Let v = .  Then\r\n" );
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document.write( "     = 12,   or\r\n" );
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document.write( "     = 0.\r\n" );
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document.write( "    Factor left side\r\n" );
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document.write( "    (v+4)*(v-3) = 0.\r\n" );
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document.write( "    As  just noticed above,  assumed to be >= 0.\r\n" );
document.write( "    Therefore, only positive root  v = 3  works.\r\n" );
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document.write( "    Thus,   = 3.   Then  x - y = 3^2 = 9.\r\n" );
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document.write( "    \r\n" );
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document.write( "3.  Thus we have two equations\r\n" );
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document.write( "    x + y = 16,\r\n" );
document.write( "    x - y =  9,\r\n" );
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document.write( "    which implies  x= 12.5,  y= 3.5.\r\n" );
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document.write( "Answer.  The solution is  x= 12.5,  y= 3.5.  The product xy = 43.75.\r\n" );
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