Aptitude Question ID : 93832

If a = 7, b = 5 and c = 3, then the value of a^{2}+b^{2}+c^{2}-ab-bc-ca is:
[A]0
[B]8
[C]-12
[D]12

12
Given Expression,
a^{2}+b^{2}+c^{2}-ab-bc-ca
=> \frac{1}{2}\left [ \left ( a-b \right )^{2}+\left ( b-c \right )^{2}+\left ( c-a \right )^{2} \right ]
=> \frac{1}{2}\left [ \left ( 7-5 \right )^{2}+\left ( 5-3 \right )^{2}+\left ( 3-7 \right )^{2} \right ]
=> \frac{1}{2}\left ( 4+4+16 \right )
=> \frac{1}{2}\times 24 = 12
Hence option [D] is the right answer.

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