If x = z = 225 and y = 226, then the value of x³ + y³ + z³ - 3xyz = ?

Solution (By Examveda Team)

According to the question,
$$\because $$ x = z = 225
y = 226
⇒ x³ + y³ + z³ - 3xyz = ?
As we know,
x³ + y³ + z³ - 3xyz
= $$\frac{1}{2}$$ (x + y + z) [(x - y)² + (y - z)² + (z - x)²]
= $$\frac{1}{2}$$ [225 + 225 + 226] [(225 - 226)² + (226 - 225)² + (225 - 225)²]
= $$\frac{676}{2}$$ × [1 + 1 + 0]
= 676