CBSE Class 9 Answered

If a = $fraction numerator square root of 5 minus 2 over denominator square root of 5 plus space 2 end fraction$ show that $a space plus space fraction numerator 1 over denominator a space end fraction space equals space 18$ and

Asked by vatsalchoudhary41 | 29 Jun, 2014, 11:17: AM

Expert Answer

$a equals fraction numerator square root of 5 minus 2 over denominator square root of 5 plus 2 end fraction text LHS end text equals a plus 1 over a equals fraction numerator square root of 5 minus 2 over denominator square root of 5 plus 2 end fraction plus fraction numerator 1 over denominator fraction numerator square root of 5 minus 2 over denominator square root of 5 plus 2 end fraction end fraction equals fraction numerator square root of 5 minus 2 over denominator square root of 5 plus 2 end fraction plus fraction numerator square root of 5 plus 2 over denominator square root of 5 minus 2 end fraction equals fraction numerator open parentheses square root of 5 minus 2 close parentheses open parentheses square root of 5 minus 2 close parentheses plus open parentheses square root of 5 plus 2 close parentheses open parentheses square root of 5 plus 2 close parentheses over denominator open parentheses square root of 5 plus 2 close parentheses open parentheses square root of 5 minus 2 close parentheses end fraction equals fraction numerator open parentheses square root of 5 minus 2 close parentheses squared plus open parentheses square root of 5 plus 2 close parentheses squared over denominator open parentheses square root of 5 close parentheses squared minus open parentheses 2 close parentheses squared end fraction equals fraction numerator open parentheses 5 minus 4 square root of 5 plus 4 close parentheses plus open parentheses 5 plus 4 square root of 5 plus 4 close parentheses over denominator 5 minus 4 end fraction equals 18 over 1 equals 18 text LHS end text equals a squared minus 1 over a squared equals open parentheses fraction numerator square root of 5 minus 2 over denominator square root of 5 plus 2 end fraction close parentheses squared minus 1 over open parentheses fraction numerator square root of 5 minus 2 over denominator square root of 5 plus 2 end fraction close parentheses squared equals open parentheses fraction numerator square root of 5 minus 2 over denominator square root of 5 plus 2 end fraction close parentheses squared minus open parentheses fraction numerator square root of 5 plus 2 over denominator square root of 5 minus 2 end fraction close parentheses squared equals open parentheses square root of 5 minus 2 close parentheses squared over open parentheses square root of 5 plus 2 close parentheses squared minus open parentheses square root of 5 plus 2 close parentheses squared over open parentheses square root of 5 minus 2 close parentheses squared equals fraction numerator 5 minus 4 square root of 5 plus 4 over denominator 5 plus 4 square root of 5 plus 4 end fraction minus fraction numerator 5 plus 4 square root of 5 plus 4 over denominator 5 minus 4 square root of 5 plus 4 end fraction equals fraction numerator 9 minus 4 square root of 5 over denominator 9 plus 4 square root of 5 end fraction minus fraction numerator 9 plus 4 square root of 5 over denominator 9 minus 4 square root of 5 end fraction equals fraction numerator open parentheses 9 minus 4 square root of 5 close parentheses open parentheses 9 minus 4 square root of 5 close parentheses minus open parentheses 9 plus 4 square root of 5 close parentheses open parentheses 9 plus 4 square root of 5 close parentheses over denominator open parentheses 9 plus 4 square root of 5 close parentheses open parentheses 9 minus 4 square root of 5 close parentheses end fraction equals fraction numerator open parentheses 9 minus 4 square root of 5 close parentheses squared minus open parentheses 9 plus 4 square root of 5 close parentheses squared over denominator open parentheses 9 close parentheses squared minus open parentheses 4 square root of 5 close parentheses squared end fraction equals fraction numerator 81 minus 72 square root of 5 plus 80 minus 81 minus 72 square root of 5 minus 80 over denominator 81 minus 80 end fraction equals fraction numerator minus 144 square root of 5 over denominator 1 end fraction equals minus 144 square root of 5$