document.write( "Question 215112: let a and b be two real numbers with a does not equal b. write an expression that will give the larger of the two numbers \n" ); document.write( "
Algebra.Com's Answer #162560 by Edwin McCravy(20055)\"\" \"About 
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let a and b be two real numbers with a does not equal b. write an expression that will give the larger of the two numbers
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document.write( "\"a%3Eb\" if and only if \"a-b=abs%28a-b%29\" if and only if \"%28a-b%29%2Fabs%28a-b%29=1\"\r\n" );
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document.write( "\"a%3Cb\" if and only if \"a-b=-abs%28a-b%29\" if and only if \"%28a-b%29%2Fabs%28a-b%29=-1\"\r\n" );
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document.write( "So we let \"x=%28a-b%29%2Fabs%28a-b%29\"\r\n" );
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document.write( "So we want a function \"f%28x%29\" such that\r\n" );
document.write( "\"f%281%29=+a\" and \"f%28-1%29=b\"\r\n" );
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document.write( "So we find the linear equation \"y=f%28x%29\" that passes through\r\n" );
document.write( "the points \"%22%28-1%2Cb%29%22\" and \"%22%281%2Ca%29%22\"\r\n" );
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document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"\r\n" );
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document.write( "\"y-b=%28%28a-b%29%2F2%29%28x-%28-1%29%29\"\r\n" );
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document.write( "\"y-b=%28%28a-b%29%2F2%29%28x%2B1%29\"\r\n" );
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document.write( "\"y=b%2B%28%28a-b%29%2F2%29%28x%2B1%29\"\r\n" );
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document.write( "\"f%28x%29=b%2B%28%28a-b%29%2F2%29%28x%2B1%29\"\r\n" );
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document.write( "So we replace \"x\" by \"%28a-b%29%2Fabs%28a-b%29\"   \r\n" );
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document.write( "\"f%28%28a-b%29%2Fabs%28a-b%29%29=b%2B%28%28a-b%29%2F2%29%28%28a-b%29%2Fabs%28a-b%29%2B1%29\"\r\n" );
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document.write( "So the right side of this equation will always give\r\n" );
document.write( "the larger of a and b:\r\n" );
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document.write( "\"b%2B%28%28a-b%29%2F2%29%28%28a-b%29%2Fabs%28a-b%29%2B1%29\"\r\n" );
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document.write( "Edwin
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