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Question: The rationalizing factor of \(a^{1/3} + a^{- 1/3}\)is...

The rationalizing factor of a1/3+a−1/3a^{1/3} + a^{- 1/3}is

A

a1/3−a−1/3a^{1/3} - a^{- 1/3}

B

a2/3+a−2/3a^{2/3} + a^{- 2/3}

C

a2/3−a−2/3a^{2/3} - a^{- 2/3}

D

a2/3+a−2/3−1a^{2/3} + a^{- 2/3} - 1

Answer

a2/3+a−2/3a^{2/3} + a^{- 2/3}

Explanation

Solution

Letx=a1/3,y=a−1/3x = a^{1/3},y = a^{- 1/3}then a=x3,a−1=y3a = x^{3},a^{- 1} = y^{3}

x3+y3=(x+y)(x2−xy+y2)x^{3} + y^{3} = (x + y)(x^{2} - xy + y^{2})

So rationlising factor is (x2−xy+y2)(x^{2} - xy + y^{2}). Put the value of x and y. Thus the required rationlising factor is a2/3+a−2/3−1a^{2/3} + a^{- 2/3} - 1.