Question

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

Answer 1

Hope this helps you☺️☺️☺️

Answer 2

Solution :

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We know that ,

If x + y + z = 0 , then

x³ + y³ + z³ = 3xyz

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Here ,

( 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

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