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Asked by yadavbrajkishore678 | 3rd Sep, 2018, 02:16: PM

Expert Answer:

$begin mathsize 16px style straight a space equals space fraction numerator square root of 5 space plus space 1 over denominator square root of 5 space minus 1 space end fraction space and space space straight b space equals space fraction numerator square root of 5 space minus space 1 over denominator square root of 5 space plus space 1 end fraction straight a over straight b equals space open parentheses square root of 5 space plus space 1 close parentheses squared over open parentheses square root of 5 space minus space 1 close parentheses squared space space space space space equals space fraction numerator 5 space plus space 2 square root of 5 space plus space 1 over denominator 5 space minus space 2 square root of 5 space plus space 1 end fraction space space space space space equals space fraction numerator 6 space plus space 2 square root of 5 space over denominator 6 space minus space 2 square root of 5 end fraction cross times space fraction numerator 6 space plus space 2 square root of 5 space over denominator 6 space minus space 2 square root of 5 end fraction...... rationalizing space the space denominator space space space space equals fraction numerator 36 space plus space 24 square root of 5 space plus space 20 over denominator 36 space minus space 20 end fraction space space space space equals fraction numerator 56 plus 24 square root of 5 over denominator 16 end fraction space equals space fraction numerator 7 plus 3 square root of 5 over denominator 2 end fraction...... left parenthesis 1 right parenthesis To space find colon space fraction numerator straight a squared space plus space ab space plus space straight b squared over denominator straight a squared space minus space ab space plus space straight b squared end fraction divide space numerator space and space denominator space by space straight b squared comma space we space get fraction numerator straight a squared space plus space ab space plus space straight b squared over denominator straight a squared space minus space ab space plus space straight b squared end fraction equals space fraction numerator space space begin display style straight a squared over straight b squared end style plus space begin display style straight a over straight b end style space plus 1 over denominator space straight a squared over straight b squared minus space straight a over straight b space plus 1 end fraction equals space fraction numerator begin display style open parentheses 7 plus 3 square root of 5 close parentheses squared over 4 end style plus fraction numerator 7 plus 3 square root of 5 over denominator 2 end fraction space plus space 1 over denominator open parentheses 7 plus 3 square root of 5 close parentheses squared over 4 minus fraction numerator 7 plus 3 square root of 5 over denominator 2 end fraction space plus space 1 end fraction equals fraction numerator open parentheses 7 plus 3 square root of 5 close parentheses squared plus space 2 open parentheses 7 plus 3 square root of 5 close parentheses plus space 4 over denominator open parentheses 7 plus 3 square root of 5 close parentheses squared minus space 2 open parentheses 7 plus 3 square root of 5 close parentheses plus space 4 end fraction equals fraction numerator 112 space plus space 48 square root of 5 over denominator 84 space plus space 36 square root of 5 end fraction Rationalize space the space denominator space by space multiplying space numerator space and space denominator space by space 84 space minus space 36 square root of 5. equals 4 over 3 space space space space space end style$

Answered by Yasmeen Khan | 3rd Sep, 2018, 03:17: PM

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