SSC CGL Tier II 25 Oct 2015 Paper 1

Question : 85 of 100

Marks: +1, -0

then the relation between a, b and c is

Solution:

(4)

3 a^{2}+3 b^{2}+3 c^{2}=(a+b+c)^{2}

⇒ 3 a^{2}+3 b^{2}+3 c^{2}=a^{2}+b^{2}+c^{2}

+2 a b+2 b c+2 a c

⇒ 3 a^{2}+3 b^{2}+3 c^{2}-a^{2}-b^{2}-c^{2}

-2 a b-2 b c-2 a c=0

⇒ 2 a^{2}+2 b^{2}+2 c^{2}-2 a b-2 b c-

2 a c=0

⇒a^{2}+b^{2}-2 a b+b^{2}+c^{2}-2 b c +a^{2}+c^{2}-2 a c=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 = b = c

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