ICSE Class 10 Answered

Asked by Topperlearning User | 14 Sep, 2017, 10:07: AM

Expert Answer

$begin mathsize 12px style straight x space equals space fraction numerator square root of straight a space plus space 3 straight b end root space plus space square root of straight a space minus space 3 straight b end root over denominator square root of straight a space plus space 3 straight b end root space minus space square root of straight a space minus space 3 straight b end root end fraction Applying space componendo space and space dividendo comma fraction numerator straight x space plus space 1 over denominator straight x space minus space 1 end fraction space equals space fraction numerator 2 square root of straight a space plus space 3 straight b end root over denominator 2 square root of straight a space minus space 3 straight b end root end fraction open parentheses straight x space plus space 1 close parentheses squared over open parentheses straight x space minus space 1 close parentheses squared space equals space fraction numerator straight a space plus space 3 straight b over denominator straight a space minus space 3 straight b end fraction fraction numerator straight x to the power of 2 space end exponent space plus space 2 straight x space plus space 1 over denominator straight x to the power of 2 space end exponent space minus space 2 straight x space plus space 1 end fraction equals space fraction numerator straight a space plus space 3 straight b over denominator straight a space minus space 3 straight b end fraction Again space applying space componendo space and space dividendo comma fraction numerator 2 straight x squared space plus space 2 over denominator 4 straight x end fraction space equals space fraction numerator 2 straight a over denominator 6 straight b end fraction fraction numerator straight x squared space plus space 1 over denominator 2 straight x end fraction space equals space fraction numerator straight a over denominator 3 straight b end fraction 3 bx squared space plus space 3 straight b space equals space 2 ax 3 bx squared space minus 2 ax space plus space 3 straight b space equals space 0 end style$