ICSE Class 9 Answered

$begin mathsize 12px style If space straight x equals 2 to the power of 1 third end exponent plus 2 to the power of fraction numerator negative 1 over denominator 3 end fraction end exponent space prove space that space 2 straight x cubed equals 6 straight x plus 5 end style$

Asked by Topperlearning User | 07 Aug, 2017, 08:43: AM

Expert Answer

$begin mathsize 12px style straight x equals 2 to the power of 1 third end exponent plus 2 to the power of fraction numerator negative 1 over denominator 3 end fraction end exponent space On space cubing space both space sides comma straight x cubed equals open parentheses 2 to the power of 1 third end exponent close parentheses cubed plus open parentheses 2 to the power of fraction numerator negative 1 over denominator 3 end fraction end exponent close parentheses squared plus 3 cross times 2 to the power of 1 third end exponent cross times 2 to the power of fraction numerator negative 1 over denominator 3 end fraction end exponent open parentheses 2 to the power of 1 third end exponent plus 2 to the power of fraction numerator negative 1 over denominator 3 end fraction end exponent space close parentheses space space space space space open square brackets By space using space open parentheses straight a plus straight b close parentheses cubed equals straight a cubed plus straight b cubed plus 3 ab open parentheses straight a plus straight b close parentheses close square brackets straight x cubed equals 2 plus 2 to the power of negative 1 end exponent plus 3 space cross times space 2 to the power of 0 space cross times space straight x straight x cubed equals 2 plus 1 half plus 3 straight x 2 straight x cubed equals 5 plus 6 straight x 2 straight x cubed equals 6 straight x plus 5 space space space space space space space space space space space space space space space space space end style$