document.write( "Question 79742: What is an extraneous solutions? \n" ); document.write( "
Algebra.Com's Answer #57217 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "What is an extraneous solutions?\r\n" );
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document.write( "It's a \"phony\" solution that you get sometimes,\r\n" );
document.write( "Even though you haven't made a mistake at all, it \r\n" );
document.write( "does not check when substituted into the original\r\n" );
document.write( "equation. \r\n" );
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document.write( "Tutor Paul above gave an example of a radical \r\n" );
document.write( "equation which has an extraneous solution. However,\r\n" );
document.write( "when you study extraneous solutions for the first \r\n" );
document.write( "time, most likely you haven't studied radical \r\n" );
document.write( "equations yet, but only rational equations.  So\r\n" );
document.write( "I think these examples would be more in line\r\n" );
document.write( "with what you are studying in school.  I'm\r\n" );
document.write( "guessing Paul's examples above are more\r\n" );
document.write( "advanced that where you are in the course at the\r\n" );
document.write( "present time, so I give these 2 examples:  \r\n" );
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document.write( "Example 1:\r\n" );
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document.write( "When you clear of fractions and solve the\r\n" );
document.write( "equation, you get the \"solution\" x = 1 \r\n" );
document.write( "However x = 1 does not check because it \r\n" );
document.write( "results in a denominator being 0, which \r\n" );
document.write( "is undefined.  So the equation has no\r\n" );
document.write( "solution at all! x = 1 is called an\r\n" );
document.write( "EXTRANEOUS solution, which is really\r\n" );
document.write( "not a solution at all.\r\n" );
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document.write( "Example 2:\r\n" );
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document.write( "When you multiply through by the LCD\r\n" );
document.write( "and solve the resulting quadratic\r\n" );
document.write( "equation, you get solutions x=2 and\r\n" );
document.write( "x=1. However when we try to check the\r\n" );
document.write( "solution x=2, it causes the first \r\n" );
document.write( "and last denominators to become 0, which\r\n" );
document.write( "is undefined.  However x=1 checks.  So\r\n" );
document.write( "we discard the extraneous solution x=2\r\n" );
document.write( "and keep the x=1 as the only solution.\r\n" );
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document.write( "Edwin
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