2015 · Q45
If x+y+z=0 then x³+y³+z³+3xyz is equal to
Elementary MathematicsAlgebra
- A0
- B6 xyz
- C12 xyz
- Dxyz
Explanation
x³+y³+z³ − 3xyz = (x+y+z)(x²+y²+z²−xy−yz−zx) = 0 when x+y+z = 0, so x³+y³+z³ = 3xyz and x³+y³+z³+3xyz = 6xyz (option B).
If x+y+z=0 then x³+y³+z³+3xyz is equal to
Explanation
x³+y³+z³ − 3xyz = (x+y+z)(x²+y²+z²−xy−yz−zx) = 0 when x+y+z = 0, so x³+y³+z³ = 3xyz and x³+y³+z³+3xyz = 6xyz (option B).