Question

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

Answer 1

If x + y + z = 0 , then  

x³ + y³ + z³ = 3xyz

( 1/2 )³+( 1/3 )³ - ( 5/6 )³

= ( 1/2 )³ + ( 1/3 )³ + ( -5/6 )³

x = 1/2 , y = 1/3 , z = -5/6

Now ,

x + y + z

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

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

= ( 3 + 2 - 5 )/6 [ Since LCM = 6 ]

= 0/6

= 0

( 1/2 )³ + ( 1/3 )³ + ( -5/6 )³

= 3xyz

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

= - 5/12

Therefore ,

( 1/2 )³ + ( 1/3 )³ + ( -5/6 )³

= -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.