Let x, y, z be positive real numbers such that x + y + z = 12 and x³y⁴z⁵ = (0.1)(600)³. Then x³ + y³ + z³ is equal to:

Given, x + y + z = 12
And, x³y⁴z⁵ = 60 × 600 × 600
Factorize it
x³y⁴z⁵ = 6³ × 10⁵ = 2³ × 3³ × 2⁵ × 5⁵ = 2⁸ × 3³ × 5⁵ = 3³ × 4⁴ × 5⁵
Let x = 3, y = 4, z = 5
Then x + y + z = 3 + 4 + 5 = 12
x³y⁴z⁵ = 3³ × 4⁴ × 5⁵ = 27 × 256 × 3125 = 21600000
(0.1)(600)³ = 0.1 × 216000000 = 21600000
x³ + y³ + z³ = 3³ + 4³ + 5³ = 27 + 64 + 125 = 216