Question

Without actual calculating the cubes find the value of 1 by 2 whole cube + 1 by 3 whole cube minus 5 by 6 whole cube

Answer 1

Hi ,

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If x + y + z = 0 then

x³ + y³ + z³ = 3xyz

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Here ,

x = 1/2 ,

y = 1/3 ,

z = - 5/6

x + y + z

= 1/2 + 1/3 - 5/6

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

= 5/6 - 5/6

= 0 ,

Therefore ,

x³ + y³ + z³

= ( 1/2 )³ + ( 1/3 )³ + ( -5/6 )³

= 3 × ( 1/2 ) × ( 1/3 ) × ( -5/6 )

= - ( 3 × 5 )/ ( 2 × 3 × 6 )

= -5/12

I hope this helps you.

: )

Answer 2

Answer:

the answer is minus 5 by 12