Question
If x = 222, y = 223, z = 225, then the value of x3 + y3 + z3 - 3xyz is?
Answer: Option B
$${x^3} + {y^3} + {z^3} - 3xyz$$
$$ = \frac{1}{2}\left( {x + y + z} \right)$$ $$\left[ {{{\left( {x - y} \right)}^2} + {{\left( {y - z} \right)}^2} + {{\left( {z - x} \right)}^2}} \right]$$
$$ = \frac{1}{2}\left( {222 + 223 + 225} \right)$$ $$\left[ {{{\left( {222 - 223} \right)}^2} + {{\left( {223 - 225} \right)}^2} + {{\left( {225 - 222} \right)}^2}} \right]$$
$$\eqalign{
& = \frac{1}{2}\left( {670} \right)\left( {1 + 4 + 9} \right) \cr
& = \frac{1}{2} \times 670 \times 14 \cr
& = 4690 \cr} $$
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$${x^3} + {y^3} + {z^3} - 3xyz$$
$$ = \frac{1}{2}\left( {x + y + z} \right)$$ $$\left[ {{{\left( {x - y} \right)}^2} + {{\left( {y - z} \right)}^2} + {{\left( {z - x} \right)}^2}} \right]$$
$$ = \frac{1}{2}\left( {222 + 223 + 225} \right)$$ $$\left[ {{{\left( {222 - 223} \right)}^2} + {{\left( {223 - 225} \right)}^2} + {{\left( {225 - 222} \right)}^2}} \right]$$
$$\eqalign{
& = \frac{1}{2}\left( {670} \right)\left( {1 + 4 + 9} \right) \cr
& = \frac{1}{2} \times 670 \times 14 \cr
& = 4690 \cr} $$
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