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सिद्ध कीजिए की |{:(,a,b,c),(,a-b,b-c,c-a...

सिद्ध कीजिए की `|{:(,a,b,c),(,a-b,b-c,c-a),(,b-c,c+a,a+b):}|=a^(3)+b^(3)+c^(3)-3abc`

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|(1,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=a^(3)+b^(3)+c^(3)-3ab

Prove that |(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)| = a^(3) + b^(3) + c^(3) - 3abc .

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Prove that : |{:(a,b,c),(b,c,a),(c,a,b):}|=3 a b c-a^(3)-b^(3)-c^(3)

Show that |(b+c,c+a,a+b),(a+b,b+c,c+a)(a,b,c)|=a^(3)+b^(3)+c^(3)-3abc .

Show that abs((a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)) = a^3+b^3+c^3 -3abc.

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Without expanding, prove the following |(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=a^3+b^3+c^3-3abc