document.write( "Question 1113566: if x=2+root3/2-root3 then find the value of x+1/x \n" ); document.write( "
Algebra.Com's Answer #728635 by ikleyn(52781)\"\" \"About 
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document.write( "  x = \"%282%2Bsqrt%283%29%29%2F%282-sqrt%283%29%29\" = rationalize the fraction = \"%282%2Bsqrt%283%29%29%2F%282-sqrt%283%29%29\" . \"%282%2Bsqrt%283%29%29%2F%282%2Bsqrt%283%29%29\"  = \"%282%2Bsqrt%283%29%29%5E2%2F%282%5E2+-+%28sqrt%283%29%29%5E2%29\"  =  \"%284+%2B+4%2Asqrt%283%29+%2B+3%29%2F%284-3%29\" = \"7%2B4%2Asqrt%283%29\" .\r\n" );
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document.write( "Then  x + \"1%2Fx\" = \"7%2B4%2Asqrt%283%29\" + \"1%2F%287%2B4%2Asqrt%283%29%29\" = rationalize the fraction = \"7%2B4%2Asqrt%283%29\" + \"1%2F%287%2B4%2Asqrt%283%29%29\" . \"%287-4%2Asqrt%283%29%29%2F%287-4%2Asqrt%283%29%29\" = \r\n" );
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document.write( "= \"7%2B4%2Asqrt%283%29\"  + \"%287-4%2Asqrt%283%29%29%2F%287%5E2+-+%284%2Asqrt%283%29%29%5E2%29\" = \"7%2B4%2Asqrt%283%29\" + \"%287-4%2Asqrt%283%29%29%2F%2849+-+48%29\" = \"7%2B4%2Asqrt%283%29\" + \"7-4%2Asqrt%283%29\" = 7 + 7 = 14.\r\n" );
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document.write( "Answer.  14.\r\n" );
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\n" ); document.write( "On rationalizing fractions, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO rationalize a fraction by making its denominator free of square roots\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO rationalize a fraction by making its denominator free of cubic roots\r
\n" ); document.write( "\n" ); document.write( "    - Amazing calculations with fractions that contain quadratic irrationalities in denominators\r
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