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Factorize a 3 +b 3 + c 3 +- 3abc |
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Answer» Step-by-step explanation: If “ a3+b3+c3=3abc then find the value of (a+b+c) where a≠b≠c”? Value of (a+b+c) is zero. Why? we know, a3 + b3 + c3 - 3abc = (a + b + c )(a2 + b2 + c2 -ab - AC -bc) Now it is GIVEN that : a3 + b3 + c3 = 3abc So, a3 + b3 + c3 - 3abc = 0 (a + b + c )(a2 + b2 + c2 -ab - ac -bc) = 0 this means either (a2 + b2 + c2 -ab - ac -bc) = 0 or (a + b + c ) = 0 (a2 + b2 + c2 -ab - ac -bc) = 0 cannot be zero because: 2a² + 2b² + 2c² -2AB - 2ac - 2BC = 0 a² + 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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