document.write( "Question 375542: A student is asked to solve b^2 + x^2 = a2 and gives the following solution.\r
\n" ); document.write( "\n" ); document.write( "b^2 + x^2 = a^2\r
\n" ); document.write( "\n" ); document.write( "√b^2+x^2 = √a^2\r
\n" ); document.write( "\n" ); document.write( "b + x = a\r
\n" ); document.write( "\n" ); document.write( "x = a - b\r
\n" ); document.write( "\n" ); document.write( "Find the multiple mistakes the student made and explain why they are incorrect. \n" ); document.write( "

Algebra.Com's Answer #267087 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"b%5E2+%2B+x%5E2+=+a%5E2\"$
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document.write( "1.  This is a mistake, but not because it is mathematically illegal,\r\n" );
document.write( "for it is not mathematically illegal to take positive square roots \r\n" );
document.write( "of both sides.  However it gets nowhere and makes matters worse.  So \r\n" );
document.write( "what the student should have done instead was to have isolated the x²\r\n" );
document.write( "term, since x is what is being solved for, and x is just the square \r\n" );
document.write( "root of x².\r\n" );
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document.write( "2.  However, since the student took positive square roots of both sides,\r\n" );
document.write( "look at what illegal thing he then did: \r\n" );
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document.write( "b + x = a \r\n" );
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document.write( "He erroneously thought \"the square root of a sum is the sum of the square\r\n" );
document.write( "roots\".  But there is no such rule.  \r\n" );
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document.write( "What happened was that he mis-remembered this correct rule:\r\n" );
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document.write( "The square root of a product is the product of the square roots.\r\n" );
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document.write( "and thought he could just replace the word \"sum\" for the word \"product\"\r\n" );
document.write( "and he'd still have a correct rule.  But that doesn't work.  You cannot\r\n" );
document.write( "replace \"sum\" for \"product\" in a rule and expect the result to be a \r\n" );
document.write( "correct rule.\r\n" );
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document.write( "Here is how he should have done it:\r\n" );
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document.write( "Isolate the  term:\r\n" );
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document.write( "Since x is squared, x could be either positive or negative,\r\n" );
document.write( "so we must take both the positive and the negative square roots \r\n" );
document.write( "of the right side. That's called \"the principle of square roots\".\r\n" );
document.write( "So the two solutions are:\r\n" );
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document.write( "Edwin

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