Question

x² (y-z) + y^2(Z-x) + z² (x-y)​

Answer 1

f (x²/yz) + (y²/zx) + (z²/xy) = 3

=> x³/xyz + y³/xyz + z³/xyz = 3

=> (x³ + y³ + z³)/xyz = 3

=> x³ + y³ + z³ = 3xyz

we know, when a + b + c = 0 then , a³ + b³ + c³ = 3abc

here, x³ + y³ + z³ = 3xyz then, x + y + z = 0

so, (x + y + z)³ = (0)³ = 0

hence, (x + y + z)³ = 0