Question : If $a = 101, b = 102,$ and $c = 103$ , then $a^{2} + b^{2} + c^{2} - a b - b c - c a$ =_____
Option 1: 2
Option 2: 4
Option 3: 3
Option 4: 6

Question

Question : If $a + b + c$ = 6 and $a b + b c + c a$ = 11, then the value of $b c (b + c) + c a (c + a) + a b (a + b) + 3 a b c$ is:

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Answer 1

Correct Answer: 3

Solution : $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
$\Rightarrow (a + b + c)^{2} - 3 (a b + b c + c a) = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) - 3 (a b + b c + c a)$
Putting the values of $a, b,$ and $c$ , we get,
$\Rightarrow (101 + 102 + 103)^{2} - 3 (101 \times 102 + 102 \times 103 + 103 \times 101) = a^{2} + b^{2} + c^{2} - (a b + b c + c a)$
$\Rightarrow a^{2} + b^{2} + c^{2} - a b - b c - c a = 306^{2} - 3 (10302 + 10506 + 10403)$
$\Rightarrow a^{2} + b^{2} + c^{2} - a b - b c - c a = 93636 - 3 (31211)$
$\Rightarrow a^{2} + b^{2} + c^{2} - a b - b c - c a = 93636 - 93633$
$∴ a^{2} + b^{2} + c^{2} - a b - b c - c a = 3$
Hence, the correct answer is 3.

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Question : If a=101,b=102, and c=103, then a2+b2+c2−ab−bc−ca =_____Option 1: 2Option 2: 4Option 3: 3Option 4: 6

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Question : If $a = 101, b = 102,$ and $c = 103$ , then $a^{2} + b^{2} + c^{2} - a b - b c - c a$ =_____
Option 1: 2
Option 2: 4
Option 3: 3
Option 4: 6