document.write( "Question 1118304: x=sqrt(3+2sqrt(2)) + sqrt(3-2sqrt(2))
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Algebra.Com's Answer #733583 by Edwin McCravy(20055)\"\" \"About 
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x=sqrt(3+2sqrt(2)) + sqrt(3-2sqrt(2))
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document.write( "\"x=sqrt%283%2B2sqrt%282%29%29+%2B+sqrt%283-2sqrt%282%29%29\"\r\n" );
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document.write( "To make things easier, let\r\n" );
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document.write( "\"sqrt%283%2B2sqrt%282%29%29=A\" and \"sqrt%283-2sqrt%282%29%29=B\"\r\n" );
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document.write( "Then \r\n" );
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document.write( "\"x=A+%2B+B\"\r\n" );
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document.write( "\"x%5E2+=+%28A%2BB%29%5E2\"\r\n" );
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document.write( "\"x%5E2+=+%28A%2BB%29%28A%2BB%29\"\r\n" );
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document.write( "\"x%5E2=A%5E2%2BAB%2BAB%2BB%5E2\"\r\n" );
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document.write( "\"x%5E2=A%5E2%2B2AB%2BB%5E2\"\r\n" );
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document.write( "Now since \r\n" );
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document.write( "\"x%5E2+=+A%5E2%2B2AB%2BB%5E2\", we'll need AČ, BČ, and AB\r\n" );
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document.write( "\"A%5E2+=+%28sqrt%283%2B2sqrt%282%29%29%29%5E2\"\r\n" );
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document.write( "\"A%5E2+=+3%2B2sqrt%282%29\"\r\n" );
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document.write( "\"B%5E2+=+%28sqrt%283-2sqrt%282%29%29%29%5E2\"\r\n" );
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document.write( "\"B%5E2+=+3-2sqrt%282%29\"\r\n" );
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document.write( "\"AB+=+%28sqrt%283%2B2sqrt%282%29%29%29%28sqrt%283-2sqrt%282%29%29%29%29%29\"\r\n" );
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document.write( "\"AB+=+sqrt%28%283%2B2sqrt%282%29%29%283-2sqrt%282%29%29%29\"\r\n" );
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document.write( "\"AB+=+sqrt%28%283%2B2sqrt%282%29%29%283-2sqrt%282%29%29%29\"\r\n" );
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document.write( "\"AB+=+sqrt%289-6sqrt%282%29%2B6sqrt%282%29-4%2A2%29%29\"\r\n" );
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document.write( "\"AB+=+sqrt%289-4%2A2%29\"\r\n" );
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document.write( "\"AB+=+sqrt%289-8%29\"\r\n" );
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document.write( "\"AB+=+sqrt%281%29\"\r\n" );
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document.write( "\"AB+=+1\"\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "\"x%5E2+=+A%5E2%2B2AB%2BB%5E2\",\r\n" );
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document.write( "\"x%5E2+=+%283%2B2sqrt%282%29%29%2B2%281%29%2B%283-2sqrt%282%29%29\",\r\n" );
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document.write( "\"x%5E2+=+3%2B2sqrt%282%29%2B2%2B3-2sqrt%282%29\",\r\n" );
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document.write( "\"x%5E2+=+3%2B2%2B3\",\r\n" );
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document.write( "\"x%5E2=8\"\r\n" );
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document.write( "\"x=%22%22+%2B-+sqrt%288%29\"\r\n" );
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document.write( "But x cannot be negative.\r\n" );
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document.write( "\"x=sqrt%284%2A2%29\"\r\n" );
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document.write( "\"x=sqrt%284%29sqrt%282%29\"\r\n" );
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document.write( "\"x=2sqrt%282%29\"\r\n" );
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document.write( "Edwin
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