Question

Ifx+y+z=0, show that x + y2 + z = 3xyz.​

Answer 1

Answer:

Given x+y+z=0

⟹x+y=−z

Cubing on both sides

(x+y)

3

=(−z)

3

⟹x

3

+y

3

+3x

2

y+3xy

2

=−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

⟹x

3

+y

3

+z

3

=3xyz

Step-by-step explanation:

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Answer 2

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

Puttting $x + y + z = 0,$

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

$x³ + y³ + z³ - 3xyz = 0$

$x³ + y³+ z³ = 3xyz$

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