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Find the lengths of the sides of the tri...

Find the lengths of the sides of the triangle whose vertices are given by the equation `(z+alpha beta)^3=alpha^3`

Text Solution

Verified by Experts

The correct Answer is:
`AB=|(alpha - alpha beta)-(alpha w -alpha beta)|=sqrt3|alpha|`
`BC=|(alphaw-alpha beta)-(alpha w^2-alpha beta)|=sqrt3|alpha|`
`CA=|(alpha w^2-alpha beta)-(alpha- alpha beta)|=sqrt3|alpha|`
`therefore` AB=BC=CA
`DeltaABC` is equilateral with each side of length |`alpha`|
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