Question

If x+y+z=0 and x^3+y^3/xyz=y^3+z^3/xyz =z^3+x^3/xyz​

Answer 1

Answer:

2(3xyz) = 3 axyz

⇒a = 2

Step-by-step explanation:

we know that when x+y+z=0 then x³+y³+z³ = 3xyz

now as x³+y³/xyz = y³+z³/xyz = z³+x³/xyz = a

so x³+y³ = axyz  ......(1)

similarly y³+z³= axyz ...............(2)

and in the same way z³+x³ = axyz .................(3)

Now adding above three equation we have

2( x³+y³+z³) = 3 axyz ...............(4)

but we know that when x+y+z=0 then x³+y³+z³ = 3xyz

so equation 4 becomes

2(3xyz) = 3 axyz

⇒a = 2