Calculate. 1\ (x^(1/3)+y^(1/3))

pliwraih 2022-07-28 Answered
Calculate.
1   ( x ( 1 / 3 ) + y ( 1 / 3 ) )
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Answers (2)

Cael Cox
Answered 2022-07-29 Author has 11 answers
1 / ( x ( 1 / 3 ) + y ( 1 / 3 ) )
= ( x ( 2 / 3 ) + y ( 2 / 3 ) ( x y ) ( 1 / 3 ) ) / ( x + y )
ie. multiply and divide by ( x ( 2 / 3 ) + y ( 2 / 3 ) ( x y ) ( 1 / 3 ) ).
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Nash Frank
Answered 2022-07-30 Author has 10 answers
I assume you are required to rationalize the denominator.
Use the sum of cubes formula, x 3 + y 3 = ( x + y ) ( x 2 x y + y 2 )
for your question use x + y = ( x 1 / 3 + y 1 / 3 ) ( x 2 / 3 x 1 / 3 y 1 / 3 + y 2 / 3 )
multiply numerator and denominator by ( x 2 / 3 x 1 / 3 y 1 / 3 + y 2 / 3 )
to get ( x 2 / 3 x 1 / 3 y 1 / 3 + y 2 / 3 ) / ( x + y )
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