without actual calculating the cubes find the value of each of the following when 1 by 2 cube + 1 by 3 cube minus 5 by 6 cube
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( 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
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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Answered by
1
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.
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