If a²+b²+c²-ab-bc-ca=0, then show that a=b=c.​

Question

If a²+b²+c²-ab-bc-ca=0, then show that a=b=c.​

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Delilah 4 weeks 2021-11-03T19:43:44+00:00 1 Answer 0 views 0

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    2021-11-03T19:45:05+00:00

    Answer:

    a² + b² + c² = ab + bc + ca

    On multiplying both sides by “2”, it becomes

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

    2a² + 2b² + 2c² = 2ab + 2bc + 2ca

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

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

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

    Step-by-step explanation:

    Hope it is useful bye bye bye bye

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