If x = 555, y = 556 and z = 557, then the value of $x^3 + y^3 + z^3 - 3xyz$.
Answer & explanation
Correct answer: option 4
If x = 555
y = 556
z = 557
then the value of $x^3 + y^3 + z^3 - 3xyz$ = ?
x3 + y3 + z3 – 3xyz = \(\frac{1}{2}\) (x + y + z) [(x – y)2 + (y – z)2 + (z – x)2
x3 + y3 + z3 – 3xyz = \(\frac{1}{2}\) (555 + 556 + 557)[(555 – 556)2 + (556 – 557)2 + (557 – 555)2]
x3 + y3 + z3 – 3xyz = \(\frac{1}{2}\) × 1668 [(-1)2 + (-1)2 + (2)2]
x3 + y3 + z3 – 3xyz = 834 × (1 + 1 + 4)
x3 + y3 + z3 – 3xyz = 834 × 6
x3 + y3 + z3 – 3xyz = 5004