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ICSE Class 9 Answered

If x>0 and (x^2)+(1/(9x^2))=25/36 find (x^3)+(1/27x^3)
Asked by jebithar2015 | 27 Apr, 2019, 03:12: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight x squared plus fraction numerator 1 over denominator 9 straight x squared end fraction equals 25 over 36
Consider comma
open parentheses straight x plus fraction numerator 1 over denominator 3 straight x end fraction close parentheses squared equals straight x squared plus 2 cross times straight x cross times fraction numerator 1 over denominator 3 straight x end fraction plus fraction numerator 1 over denominator 9 straight x squared end fraction
open parentheses straight x plus fraction numerator 1 over denominator 3 straight x end fraction close parentheses squared equals straight x squared plus fraction numerator 1 over denominator 9 straight x squared end fraction plus 2 over 3
open parentheses straight x plus fraction numerator 1 over denominator 3 straight x end fraction close parentheses squared equals 25 over 36 plus 2 over 3 equals fraction numerator 25 plus 24 over denominator 36 end fraction equals 49 over 36
open parentheses straight x plus fraction numerator 1 over denominator 3 straight x end fraction close parentheses squared equals 49 over 36
straight x plus fraction numerator 1 over denominator 3 straight x end fraction equals 7 over 6
open parentheses straight x plus fraction numerator 1 over denominator 3 straight x end fraction close parentheses cubed equals straight x cubed plus 3 straight x squared cross times fraction numerator 1 over denominator 3 straight x end fraction plus 3 straight x cross times fraction numerator 1 over denominator 9 straight x squared end fraction plus fraction numerator 1 over denominator 27 straight x cubed end fraction
open parentheses straight x plus fraction numerator 1 over denominator 3 straight x end fraction close parentheses cubed equals straight x cubed plus straight x plus fraction numerator 1 over denominator 3 straight x end fraction plus fraction numerator 1 over denominator 27 straight x cubed end fraction
open parentheses 7 over 6 close parentheses cubed equals straight x cubed plus 7 over 6 plus fraction numerator 1 over denominator 27 straight x cubed end fraction
straight x cubed plus fraction numerator 1 over denominator 27 straight x cubed end fraction equals 343 over 216 plus 7 over 6 equals fraction numerator 343 plus 252 over denominator 216 end fraction equals 595 over 216








end style
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