document.write( "Question 38572: 36. Show a complete solution.\r
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Algebra.Com's Answer #24088 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Show a complete solution.\r\n" );
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document.write( "Two positive numbers differ by 11, and their square roots \r\n" );
document.write( "differ by 1.  Find the numbers.\r\n" );
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document.write( ">>...Two positive numbers differ by 11,,,<<\r\n" );
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document.write( "  x - y = 11\r\n" );
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document.write( ">>...their square roots differ by 1...<<\r\n" );
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document.write( " Öx - Öy = 1\r\n" );
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document.write( "So we have to solve the system:\r\n" );
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document.write( "  x - y = 11\r\n" );
document.write( "  _    _\r\n" );
document.write( " Öx - Öy = 1\r\n" );
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document.write( "We use substitutions. Solve the first\r\n" );
document.write( "equation for x\r\n" );
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document.write( "  x - y = 11\r\n" );
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document.write( "      x = 11 + y\r\n" );
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document.write( "Then we substitute 11 + y for x in the second equation:\r\n" );
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document.write( "  ______    _\r\n" );
document.write( " Ö11 + y - Öy = 1\r\n" );
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document.write( "Isolate the most complicated radical term:\r\n" );
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document.write( "      Ö11 + y = 1 + Öy\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "     ______           _\r\n" );
document.write( "   (Ö11 + y)² = (1 + Öy)\r\n" );
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document.write( "To square the left we only need to take away the radical\r\n" );
document.write( "because the left consists of only one radical term.\r\n" );
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document.write( "However to square the right, we must put it down two\r\n" );
document.write( "times and multiply it out using FOIL\r\n" );
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document.write( "       11 + y = (1 + Öy)(1 + Öy)\r\n" );
document.write( "                     _    _     _ \r\n" );
document.write( "       11 + y = 1 + Öy + Öy + (Öy)²\r\n" );
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document.write( "       11 + y = 1 + 2Öy + y\r\n" );
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document.write( "Isolate the radical term:\r\n" );
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document.write( "           10 = 2Öy\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( "            5 = Öy\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "           5² = (Vy)²\r\n" );
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document.write( "           25 = y\r\n" );
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document.write( "To find the other number x, we substitute 25 for y in\r\n" );
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document.write( "            x = 11 + y\r\n" );
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document.write( "            x = 11 + 25\r\n" );
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document.write( "            x = 36\r\n" );
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document.write( "So the two numbers are 36 and 25.\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "They differ by 36 - 25 or 11\r\n" );
document.write( "Their square roots are 6 and 5\r\n" );
document.write( "Their square roots differ by 6 - 5 or 1\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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