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  1. If a2 + b2 + c2 = ab + bc + ca ,then the value of
    a + c
    is
    b

    1. 0
    2. 2
    3. 1
    4. –1
Correct Option: B

a2 + b2 + c2 = ab + bc + ca
⇒ a2 + b2 + c2 - ab - bc - ca = 0
On multiplying by 2,
2a2 + 2b2 + 2c2 - 2ab - 2bc - 2ca = 0
⇒ a2 + b2 - 2ab + b2 + c2 - 2bc + c2 + a2 - 2ca = 0
⇒ (a - b)2 + (b - c)2 + (c - a)2 = 0
⇒ a – b = 0 ⇒ a = b
b – c = 0 ⇒ b = c
c – a = 0 ⇒ c = a

a + c
=
2a
= 2
ba



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