Question

hala everyone!
answer ma question in short and proper way :)

If X + Y + Z = 0 . Show that x cube + y cube + z cube equals to 3 xyz

Answer 1

$\color{blue}\huge\bold\star\underline\mathfrak{Bonjour\:Mate}\star$

$\color{violet}\huge\bold\star\underline\mathcal{Here\:Is\:Ur\:AnSwer}\star$

$\color{red}\huge\bold\star\underline\mathfrak{Màths\:Cutiee}\star$

we know,x³+y³+z³=(x+y+z)(x²+y²+z²-xy-yz-zx)+3xyz......( 1 )

»» Given x+y+z = 0

replace "x+y+z" in ( 1 )

we get,

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


»» x³+y³+z³=0+3xyz

»» x³+y³+z³=3xyz ««


$<font color="green"><marquee>☝☝èèñSha Ållàh☝☝</marquee></font>$

Answer 2

$\color{red}\huge\bold\star\underline\mathfrak{Bonjour\:Mate}\star$

$\color{violet}\huge\bold\star\underline\mathcal{Here\:Is\:Ur\:AnSwer}\star$

$\color{blue}\huge\bold\star\underline\mathfrak{Màths\:fixer}\star$

we know,

→ x³+y³+z³=(x+y+z)(x²+y²+z²-xy-yz-zx)+3xyz......( 1 )

»» Given x+y+z = 0

replace "x+y+z" in ( 1 )

we get,

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

»» x³+y³+z³=0+3xyz

»» x³+y³+z³=3xyz ««

$<font color="mahroon"><marquee>»✌✌“thanku”✌✌«</marquee></font>$