Question

a^+b^+c^-ab-bc-ca=0 then prove a=b=c

Answer 1

Step-by-step explanation:

your question is wrong bro

that's the right question

Q. a^2 +b^2 +c^2 -ab-bc-ca=0 then prove a=b=c ?

solution:-

Multiply both sides with 2, then we get

=> 2( ^a2 + b^2 + c^2 – ab – bc – ca) = 0

=> 2a^2 + 2b^2 + 2c^2 – 2ab – 2bc – 2ca = 0

=> (a^2 – 2ab + b^2) + (b^2 – 2bc + c^2) + (c^2 – 2ca + a^2) = 0

=> (a –b)^2 + (b – c)^2 + (c – a)^2 = 0

we know that,

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

=> (a –b)2 = 0, (b – c)2 = 0 and (c – a)2 = 0

=> (a –b) = 0, (b – c) = 0 and (c – a) = 0

=> a = b, b = c and c = a

∴ a = b = c

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