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Division of Polynomials

If x=997, ...

Question

If $x = 997$ , $y = 998$ , $z = 999$ , then the value of $x^{2} + y^{2} + z^{2} - x y - y z - z x$ will be:

A

3

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B

9

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C

16

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D

4

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Solution

The correct option is D $3$
Clearly $y = x + 1; z = x + 2$
So, we have to find:
$x^{2} + (x + 1)^{2} + (x + 2)^{2} - x (x + 1) - (x + 1) (x + 2) - x (x + 2)$
=> $x^{2} + x^{2} + 2 + 2 x + x^{2} + 4 + 4 x - x^{2} - x - x^{2} - 2 x - x - 2 - x^{2} - 2 x$
=> $3$

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