Question

If x = cube root (2 + square root 3), then what is x cube + 1/x cube?

Answer 1

put the value of x and then remove cube root then rationlise 1/2+√3 and put the value and solve u will get your answer as I had solve on that pic

Answer 2

x³ + 1/x³   = 4 if x = ∛(2 + √3)

Step-by-step explanation:

x = ∛(2 + √3)

x³   + 1/x³

x = ∛(2 + √3)

cubing both sides

=> x³ = 2 + √3

1/x³ = 1/(2 + √3)

Rationalizing

=> 1/x³  = {1/(2 + √3) } * {(2 - √3)/(2 + √3)}

=> 1/x³  = (2 - √3) /(4 - 3)

=>  1/x³  =  2 - √3

x³ + 1/x³   =  2 + √3 +  2 - √3

=> x³ + 1/x³   = 4

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