Question : If $x = 222, y = 223$ and $z = 224$ , then find the value of $x^{3} + y^{3} + z^{3} - 3 x y z$ .
Option 1: 2007
Option 2: 2004
Option 3: 2006
Option 4: 2005

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Question : $If x^{2} + y^{2} + z^{2} = x y + y z + z x and x = 1, then find the value of \frac{10 x^{4} + 5 y^{4} + 7 z^{4}}{13 x^{2} y^{2} + 6 y^{2} z^{2} + 3 z^{2} x^{2}}$ .

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Answer 1

Correct Answer: 2007

Solution : $x^{3} + y^{3} + z^{3} - 3 x y z = \frac{1}{2} (x + y + z) [(x - y)^{2} + (y - z)^{2} + (z - x)^{2}]$
$= (\frac{1}{2}) (222 + 223 + 224) [(222 - 223)^{2} + (223 - 224)^{2} + (224 - 222)^{2}]$
$= (\frac{1}{2}) (669) [(1) + (1) + (4)]$
$= 3 \times 669 = 2007$
Hence, the correct answer is 2007.

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Question : If x=222,y=223 and z=224, then find the value of x3+y3+z3−3xyz.Option 1: 2007Option 2: 2004Option 3: 2006Option 4: 2005

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Question : If $x = 222, y = 223$ and $z = 224$ , then find the value of $x^{3} + y^{3} + z^{3} - 3 x y z$ .
Option 1: 2007
Option 2: 2004
Option 3: 2006
Option 4: 2005