document.write( "Question 1209214: The radical $\"sqrt%28%2880%29%2Bsqrt%281776%29%29\"$ can be expressed as $\"sqrt%28a%29+%2Bsqrt%28b%29\"$ , where a < b. What is the product \"ab\"? \n" ); document.write( "

Algebra.Com's Answer #847852 by ikleyn(52809) $\"\"$ $\"About$

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\n" ); document.write( "The radical $\"sqrt%28%2880%29%2Bsqrt%281776%29%29\"$ can be expressed as $\"sqrt%28a%29+%2Bsqrt%28b%29\"$ , where a < b. What is the product \"ab\"?
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\n" ); document.write( "\n" ); document.write( "This problem is posed INCORRECTLY.\r
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\n" ); document.write( "\n" ); document.write( "It gives one equation for two variables, \"a\" and \"b\", and asks about the value of the product \"ab\".\r
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\n" ); document.write( "\n" ); document.write( "This equation has INFINITELY MANY possible solutions for \"a\" and \"b\", and,
\n" ); document.write( "respectively, there are INFINITELY MANY different possible values of \"ab\".\r
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\n" ); document.write( "\n" ); document.write( "Nevertheless, the other tutor deduces the unique value as the answer.\r
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\n" ); document.write( "\n" ); document.write( "Why ? - Because his solution is erroneous: it has an error.\r
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document.write( "The other tutor deduces this equation\r\n" );
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document.write( "    80 +  = {(a+b) + .    (1)\r\n" );
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document.write( "Till this point, everything is correct.\r\n" );
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document.write( "But in the next step, the other tutor concludes that from this equation, we have \r\n" );
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document.write( "    80 = a + b,   = .    (2)\r\n" );
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document.write( "and continues with it.\r\n" );
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document.write( "This step is an error. There is / (there are) no logical deducing from (1) to (2).\r\n" );
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document.write( "Making this logical deducing is the error.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Again, the given / (original) equation has infinitely many solutions in real numbers,
\n" ); document.write( "and they create infinitely many possible values for \"ab\".\r
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\n" ); document.write( "\n" ); document.write( "If somebody wants to create a correct problem from this, the problem's formulation must be changed:
\n" ); document.write( "more restrictions to \"a\" and \"b\" should be imposed.\r
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