Question

☘️☘️Answer
13th
question
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Answer 1

x + y + z = 0 ----- ( 1 )

x + y = - z

Cubing on both sides

( x + y )³ = ( - z )³

x³ + y³ + 3xy( x + y) = - z³

From ( 1 )

x³ + y³ + 3xy( - z) = - z³

x³ + y³ - 3xyz = - z³

x³ + y³ + z³ = 3xyz

Hence shown

Answer 2

Answer:

given

$\sf \: x+y+z=0 - - - - (1)$

then

$\sf \: x+y= -z$

cubing on both side

$\sf(x+y)^{3} = -z^{3}$

formula = $\sf(x+y)^{3} = x^{3} +3xy(x+y)+ y^{3}$

So here also

$\sf{x}^{3} + 3xy(x + y) + {y}^{3} = { - z}^{3}$

$\sf \: x ^{3} +3xy( -z)+y^3= -z^3$

Hence

$\sf \red{ \: x^3+ y^3+ z^3= 3xyz}$