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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 7th August 2017, 8:43 AM
Answered by 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

Answered by Expert 7th August 2017, 10:43 AM
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