Question

If x= 2+root3, find x^3 + 1/x^3

Answer 1

HERE IS YOU ANSWER

X = 2 + √3

SO X^3 + 1/X^3 = [X+1/X]^3 -3(X+1/X)(X×1X)

X^3 + 1/X^3 = [X+1/X]^3 - 3(X+1/X)

= [X+1X] [ (X+1/X)^2 - 3]

= [ 2+√3] [ (2+√3)^2 - 3]

= [2+√3] [ 2^2 + 2×2×√3 + (√3)^2 -3]

= [2+√3] [4+4√3+3-3]

= [2+√3] [ 4+4√3]

= 8 + 8√3 + 4√3 + 12

= 20 + 12√3 ANSWER

IDENTITIES USED

a^3 + b^3 = (a+b)^3 - 3(a+b)(ab)

(a+b)^2 = a^2 + b^2 + 2ab

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