Question

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

Answer 1

Answer:

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

If a+ b+ c=0 then, a³ + b³ + c³ = 3abc [Identity]

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

             = (3 + 2 -5) / 6

             = (5-5) / 6

             = 0/6

             = 0

Therefore, a³ + b³ + c³ = 3abc

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

                                    = -5/12 = -0.4167

Hope it helps You....

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Answer 2

Answer:

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

We know that x + y + z=0

then x³ + y³ + z³ =3xyz

x + y + z= (1/2)3 + (1/3)3 + (-5/6)3

            = 3/6 + 3/9 - 15/18

            = 15/18 - 15/18

            = 0

So,  x³ + y³ + z³ = 3xyz

                         = 3(3/6)(3/9)(-15/18)

                         = 3 × (-0.13889)

                        =  -0.41667

I hope you understand.

Step-by-step explanation: