Let a,b,c,p be rational numbers such that p is not a perfect cube.

Show that a = b = c

when a + b \times p^(1/3) + c \times p^(2/3) = 0

Please show different proofs.

Also tell me how to write mathematical terms like exponents etc. in Brilliant

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

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