Question

44. Without actual calculating the cubes, find the value of each of the following (1/2 )³ + (1/3)³- (5/6)³​

Answer 1

Step-by-step explanation:

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

x+y+z=0

X^3+y^3+z^3=3xyz

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

X+Y+Z=1/2+1/3+-5/6=3+2-5/6

=0

Therefore answer 3xyz=3(0)=0

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.