Question

If x + y + z = 0 then
x + y + 2 – 3xyz = ?
(a 1
(b) -1
(C) 2
(d) 0
please step by step explain​

Answer 1

Answer:

(d) 0

Step-by-step explanation:

x^3 + y^3 + z^3 - 3xyz = 0

Given, x^3 + y^3 + z^3 = 3xyz

Therefore, x^3 + y^3 + z^3 - 3xyz =0

This means,

x^3 + y^3 + z^3 - 3xyz = (x + y + z)•(x^2 + y^2 + z^2 - xy - yz - zx)

Now if x + y + z = 0, then......

x^3 + y^3 + z^3 - 3xyz = ( 0 ) (x^2 + y^2 + z^2 - xy - yz - zx)  . . . . . . .... ..... ... .. . . .. . .....    [ subsituting the value of x + y + z ]

x^3 + y^3 + z^3 - 3xyz = 0   

x^3 + y^3 + z^3 = 3xyz .

=> x^3 + y^3 + z^3 - 3xyz = 0

Hence, proved.