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Simple expression but difficult answer (Posted on 2013-05-21) Difficulty: 2 of 5
Which is larger

(21/3-1)1/3     or     (1/9)1/3 - (2/9)1/3 + (4/9)1/3 ?

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts numerically (spoiler) | Comment 1 of 2

Using the default precision of UBASIC:

10   Lhs=(2^(1/3)-1)^(1/3)
20   Rhs=(1/9)^(1/3)-(2/9)^(1/3)+(4/9)^(1/3)
30   print Lhs
40   print Rhs



which looks like the difference is only rounding error.

This can be confirmed by increasing the precision:

point 16
Words for fractionals 16 (Decimals for display 77)

which pushes the rounding error further down the line.

It seems both formulae represent the same value.

  Posted by Charlie on 2013-05-21 13:28:37
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