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Rita the dog
Lv 7
Prove the following identity involving pi?
Update:
Surely this shows that π is an algebraic number.
:)
1 Answer
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- DukeLv 76 years agoFavorite Answer
Even more: every number (say x) is algebraic, transcendent numbers do not exist at all - see the proof below:
∛( 4(x² + 1)√(x² + 4) + 4x³ + 12x ) - ∛( 4(x² + 1)√(x² + 4) - 4x³ - 12x ) =
= ∛( (√(x² + 4) + x)³ ) - ∛( (√(x² + 4) - x)³ ) =
= (√(x² + 4) + x) - (√(x² + 4) - x) = x - (-x) = 2x; now take any Greek (or whatever you like - Cyrillic, Chinese, etc.) letter instead of x.
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