Question

If X+y+z=0 then find the value of X x cube + y cube + z cube is equal to

Answer 1

Answer:

x³+y³+z³= 3xyz

Step-by-step explanation:

x³+y³+z³-3xyz = ( x+y+z) ( x²+ y²+ z² - xy - yz - zx)

x³+ y³+ z³-3xyz = (0) ( x²+ y²+ z² - xy - yz - zx)

x³+ y³+ z³-3xyz= 0

x³+ y³+ z³= + 3xyz Ans

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Answer 2

Step-by-step explanation:

x+y+z=0⇒x+y=−z

Cubing on both sides,

(x+y)

3

=(−z)

3

⇒x

3

+y

3

+3xy(x+y)=z

3

⇒x

3

+y

3

+3xy(−z)=−z

3

⇒x

3

+y

3

−3xyz+z

3

=0

∴x

3

+y

3

+z

3

=3xyz