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) हे + 02 +0 न 390८ डाएन (2 + 90 + दो “अं माने डिगाव का निधि (8 # ७ * 2)मद |
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Answer» a^3 + b^3 + c^3 - 3abc = (a + b + c )(a^2 + b^2 + c^2 -ab - ac -bc) Now it is given that : a^3 + b^3 + c^3 = 3abcSo, a^3 + b^3 + c^3 - 3abc = 0(a + b + c )(a^2 + b^2 + c^2 -ab - ac -bc) = 0 this means either(a^2 + b^2 + c^2 -ab - ac -bc) = 0 or (a + b + c ) = 0 (a^2 + b^2 + c^2 -ab - ac -bc) = 0 cannot be zero because:2a² + 2b² + 2c² -2ab - 2ac - 2bc = 0a² + b² -2ab + a² +b² +2c² - 2ac -2bc = 0(a-b)² + a² + c² -2ac + b² + c² -2bc = 0(a-b)² + (a-c)² + (b-c)² = 0 (a-b)² , (a-c)² ,(b-c)² >=0 As a≠b≠c , The given value cannot be zero. This means(a + b + c ) has to be zero |
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