if a^2+b^2+c^2=(a+b+c)^2 then ab+BC+ca=?
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Iodine is a non metal which is lustrous in nature. A non metal which exists in liquid state at room temperature is bromine. Graphite, an allotrope of carbon is the non metal which is the conductor of electricity. 5(me 0035836
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Step-by-step explanation:
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.
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