ICSE Class 10 Answered

Asked by Topperlearning User | 14 Sep, 2017, 10:30: AM

Expert Answer

$begin mathsize 12px style straight y space equals fraction numerator open parentheses straight p plus 1 close parentheses to the power of begin display style fraction numerator 1 over denominator 3 space end fraction end style end exponent plus space open parentheses straight p minus 1 close parentheses to the power of fraction numerator 1 over denominator 3 space end fraction end exponent space over denominator open parentheses straight p plus 1 close parentheses to the power of fraction numerator 1 over denominator 3 space end fraction end exponent minus space open parentheses straight p minus 1 close parentheses to the power of fraction numerator 1 over denominator 3 space end fraction end exponent space end fraction fraction numerator straight y space plus thin space 1 over denominator straight y space minus space 1 end fraction equals fraction numerator 2 open parentheses straight p plus 1 close parentheses to the power of fraction numerator 1 over denominator 3 space end fraction end exponent space over denominator 2 open parentheses straight p space minus 1 close parentheses to the power of fraction numerator 1 over denominator 3 space end fraction end exponent end fraction space space space space space space left parenthesis by space componendo space and space dividendo right parenthesis open parentheses straight y space plus thin space 1 close parentheses cubed over open parentheses straight y space minus space 1 close parentheses cubed equals fraction numerator open parentheses straight p plus 1 close parentheses space over denominator open parentheses straight p space minus 1 close parentheses end fraction space space space space space space space space left parenthesis cubing space both space sides right parenthesis fraction numerator straight y cubed space plus space 3 straight y squared space plus space 3 straight y space plus space 1 over denominator straight y cubed space minus space 3 straight y squared space plus space 3 straight y space minus space 1 end fraction space equals space fraction numerator space straight p space plus space 1 over denominator straight p space minus space 1 end fraction fraction numerator 2 straight y cubed space plus space 6 straight y over denominator 6 straight y squared space plus space 2 end fraction space equals space fraction numerator 2 straight p over denominator 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis by space componendo space and space dividendo right parenthesis straight y cubed space plus space 3 straight y space equals space straight p space open parentheses 3 straight y squared space plus space 1 close parentheses straight y cubed space minus space 3 py squared space plus space 3 straight y space minus space straight p space equals space 0 end style$