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[✓] Calculate the following mathematical expression in W|A?

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Hello, I am a new user and this is my first post; I'm from Italy (sorry for bad English); I have difficulty in put this data into the online calculator enter image description here

This is my input data

(2a-(√4(a)^2)^1/3)/(√2a-(√2a)^(1/3)

I haven't understood yet how to modify the syntax

Is there someone who could help me??? Thanks!!!

POSTED BY: Andrea Hamari
Answer
2 months ago

This is awesome! Thanks!!!

POSTED BY: Andrea Hamari
Answer
2 months ago

Hi, there is another issue... the syntax now is correct but the results is wrong (and step by step feature is not available). What's wrong? Is the syntax processed incorrectly (so it's wrong despite it appears ok) or there is a bug in the online calculator?

This should be the expected result enter image description here

POSTED BY: Andrea Hamari
Answer
2 months ago

Hi,

there is not bug in the Wolfram|Alpha. But your expected result is not a general result; i.e you make additional assumptions. If you assume that a is a real number that is positive then the term simplifies to yours. But if a<0 for example Wolfram|Alpha's solution is more appropriate.

If you go to one of the (free) cloud products (not Wolfram|alpha) and type in:

FullSimplify[(2 a - (4 a^2)^(1/3))/(Sqrt[2 a] - (2 a)^(1/3)),   Assumptions -> a \[Element] Reals && a > 0 ]

you will get the result you expect. For example:

Simplify[2^(1/3) a^(1/3) + Sqrt[2] Sqrt[a] == (2 a - (4 a^2)^(1/3))/(Sqrt[2 a] - (2 a)^(1/3)),Assumptions -> a \[Element] Reals && a > 0 ]

evaluates to True, whereas

Simplify[2^(1/3) a^(1/3) + Sqrt[2] Sqrt[a] == (2 a - (4 a^2)^(1/3))/(Sqrt[2 a] - (2 a)^(1/3))]

evaluates to

(a^(2/3) - (a^2)^(1/3))/((-1 + 2^(1/6) a^(1/6)) a^(1/6)) == 0

Cheers,

Marco

POSTED BY: Marco Thiel
Answer
2 months ago

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