Question

please answer the question

Answer 1

The roots are equal, so the discriminant is 0.

(b - c)^2 - (4(a - b)(c - a)) = 0

=> (b^2 - 2bc + c^2) - (4(ac - a^2 - bc + ab)) = 0

=> b^2 - 2bc + c^2 - (4ac - 4a^2 - 4bc + 4ab) = 0

=> b^2 - 2bc + c^2 - 4ac + 4a^2 + 4bc - 4ab = 0

=> 4a^2 + b^2 + c^2 - 4ab + 2bc - 4ac = 0

=> (2a - b - c)^2 = 0

=> 2a - b - c = 0

=> 2a = b + c

Hence proved!

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