i did not understand how did a^2+b^2+c^2-ab-bc-ca+0 come?????last fourth step…

Question

i did not understand how did a^2+b^2+c^2-ab-bc-ca+0 come?????last fourth step…

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Sarah 1 month 2021-08-17T21:14:45+00:00 1 Answer 0 views 0

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    2021-08-17T21:16:17+00:00

    Answer:

     a² + b² + c² – ab – bc – ca = 0

    Multiply both sides with 2, we get

    2( a² + b² + c² – ab – bc – ca) = 0

    ⇒ 2a² + 2b² + 2c² – 2ab – 2bc – 2ca = 0

    ⇒ (a² – 2ab + b²) + (b² – 2bc + c²) + (c² – 2ca + a²) = 0

    ⇒ (a –b)² + (b – c)² + (c – a)² = 0

    Since the sum of square is zero then each term should be zero

    ⇒ (a –b)² = 0,  (b – c)² = 0, (c – a)² = 0

    ⇒ (a –b) = 0,  (b – c) = 0, (c – a) = 0

    ⇒ a = b,  b = c, c = a

    ∴ a = b = c.

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