if x=cube root of 2 plus square root of 3 end root,find the value of straight x cubed

+1/x

Asked by sppsatya1998 | 25th Apr, 2019, 10:38: PM

Expert Answer:

G i v e n colon space x equals cube root of 2 plus square root of 3 end root
rightwards double arrow x cubed equals 2 plus square root of 3
N o w comma space x cubed plus 1 over x equals 2 plus square root of 3 plus fraction numerator 1 over denominator cube root of 2 plus square root of 3 end root end fraction
space space space space space space space space space equals 2 plus square root of 3 plus fraction numerator 1 over denominator cube root of 2 plus square root of 3 end root end fraction cross times fraction numerator cube root of 2 minus square root of 3 end root over denominator cube root of 2 minus square root of 3 end root end fraction
space space space space space space space space space equals 2 plus square root of 3 plus fraction numerator cube root of 2 minus square root of 3 end root over denominator 1 end fraction
space space space space space space space space space equals 2 plus square root of 3 plus cube root of 2 minus square root of 3 end root

A l s o comma space i f space x cubed space i s space t a k e n space i n s t e a d space o f space x comma space t h e n space w e space a r r i v e space a t space t h e space s i m p l e r space v a l u e
x cubed plus 1 over x equals 2 plus square root of 3 plus fraction numerator 1 over denominator 2 plus square root of 3 end fraction
space space space space space space space space space equals 2 plus square root of 3 plus fraction numerator 1 over denominator 2 plus square root of 3 end fraction cross times fraction numerator 2 minus square root of 3 over denominator 2 minus square root of 3 end fraction
space space space space space space space space space equals 2 plus square root of 3 plus fraction numerator 2 minus square root of 3 over denominator 1 end fraction
space space space space space space space space space equals 4

Answered by Renu Varma | 26th Apr, 2019, 10:31: AM

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