Question

Rationalizing Factor of

5^1/3+5^-1/3 is ...?

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Answer 1

Using the identity,

${x} ^{3} + {y} ^{3}$ = ( x - y) (${x} ^{2}$ + ${y} ^{2}$- xy)

Now, x = ${5}^{1/3}$ and y = ${5}^{-1/3}$

${5} ^{1/3*3} + {5} ^{-1/3*3}$ = (${5}^{1/3}$ - ${5}^{-1/3}$) (${5} ^{2*1/3}$ + ${5} ^{-2*1/3}$- ${5}^{-1/3}$*${5}^{1/3}$ )

Rationalising factor = Second factor of

R.H.S. = ${5} ^{2/3}$ + ${5} ^{-2/3}$- ${5}^{0}$

Rationalising factor = ${5} ^{2/3}$ + ${5} ^{-2/3}$- 1