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Answers
Answer:
Follow the steps given below
Step-by-step explanation:
Solution :
***************************************
We know that ,
If x + y + z = 0 , then
x³ + y³ + z³ = 3xyz
****************************************
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
Hope this answer will helps you.
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Answer:
-5/12
Step-by-step explanation:
(1/2)³ +(1/3)³-(5/6)³
let x=1/2,y=1/3,z=-5/6
x+y+z=1/2+1/3-5/6
=1/6(3+2-5)
x+y+z=0
We know if x+y+z=0
then x³+y³+z³=3xyz
putting values of x,y,z
(1/2)³+(1/3³+(-5/6)³=3*1/2*1/3*(-5/6)
(1/2)³+(1/3³-(5/6)³=-15/36