if the two roots of the equation (a-b)x2 + (b-c) x + (c-a) =0 are equal. prove that 2a=b+c
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The two roots are equal
=> discriminant = 0
=> (b-c)² - 4(a-b)(c-a) = 0
=> b² - 2bc + c² - 4ac + 4a² + 4bc - 4ab = 0
=> b² + 2bc + c² - 4ac + 4a² - 4ab = 0
=> (b+c)² - 4a(b+c) + 4a² = 0
=> ( (b+c) - 2a )² = 0
=> b+c - 2a = 0
=> 2a = b+c
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