If a^{2}+ b^{2} + c^{2} = ab + bc + ca, then the value of \frac{a+c}{b} is

SSC CPO SI and ASI 2015 Paper

Question : 138 of 199

Marks: +1, -0

If a

^{2}

+ b

^{2}

+ c

^{2}

= ab + bc + ca, then the value of

\ {a+c}/{b}

Solution:

(2)

a^{2}+b^{2}+c^{2}=a b+b c+c a-0

2 a^{2}+2 b^{2}+2 c^{2}-2 a b-2 b c-2 c a=0

a^{2}+b^{2}-2 a b+b^{2}+c^{2}-2 b c+c^{2}+a^{2}-2 c a=0

(a-b)^{2}+(b-c)^{2}+(c-a)^{2}=0 ⇒a=b=c

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