Q. 205.0( 4 Votes )

# If a, b are ratio

Answer :

a2 + b2 + c2 – ab – bc – ca = 0

Multiplying both sides by 2 we get

2 (a2 + b2 + c2 – ab – bc – ca ) = 0

(a2 + b2 - 2ab) + ( b2 + c2 - 2bc) + (c2 + a2 -2ac) = 0

The individual terms inside the brackets can be expressed as a whole square

(a – b)2 + (b – c)2 + (c – a)2 = 0

Since a, b, c are rational and none of the term is equal to zero so each of the terms inside the bracket must individually be equal to zero

a – b = 0

a = b

b – c = 0

b = c

c – a = 0

c = a

So together we can say that

a = b = c

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