Question

without actually calculateing cubes find the value (1/2)³+(1/3)³-(5/6)³

Answer 1

Answer:

-5/12 .... without calculating............

Answer 2

Step-by-step explanation:

Solution:

Given

(1/2)³ + (1/3)³ - (5/6)³

Let a = 1/2, b = 1/3, c = -(5/6)

∴ a + b + c = (1/2) + (1/3) - 5/6

= (3 + 2 - 5)/6

= 0/6 = 0

→ a³ + b³ + c³ = 3abc

∴ (1/2)³ + (1/3)³ - (5/6)³

= (1/2)³ + (1/3)³ + [-(5/6)]³

= 3 × (1/2) × (1/3) × [-(5/6)]

= -(5/12) Ans.