Question

Without actually calculating the cubes, find the value of
(1/2)³+(1/3)³-(5/6)³
​

Answer 1

Answer:

-5/12

We know that, if a+b+c = 0,

then a³+b³+c³ = 3abc

Since 1/2+1/3+(-5/6) = 0, so (Taking the minus side inside and cubing also gives negative)

(1/2)³+(1/3)³+(-5/6)³ = 3(1/2)(1/3)(-5/6)

= -5/12

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.