Question

How to evaluate ( 1/2)power 3+(1/3)power 3=(5/6)power 3

Answer 1

Hi ,

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we know the algebraic identity,

a³ + b³ = ( a + b )³ - 3ab( a + b )

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Let a = 1/2

b = 1/3 ,

a + b = 1/2 + 1/3

= ( 3 + 2 )/6

= 5/6

Now ,

.LHS = ( 1/2 )³ + ( 1/3 )³

= ( 1/2 + 1/3 )³ - 3 × 1/2 × 1/3 ( 1/2 + 1/3 )

= ( 5/6 )³ - 3 × 1/6 × 5/6

= ( 5/6 ) [ ( 5/6 )² - 1/2 ]

= ( 5/6 ) [ 25/36 - 1/2 ]

= ( 5/6 ) [ ( 25 - 18 ) / 36 ]

= ( 5/6 ) ( 7/36 )

= 35/6³

I hope this helps you


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