Eduprobe
Question:
If x+y+z=0, show that x³+y³+z³=3xyz
Solution:
We know that x³+y³+z³−3xyz=(x+y+z)(x²+y²+z²−xy−yz−zx)
Given x+y+z=0
x³+y³+z³−3xyz=(0)(x²+y²+z²−xy−yz−zx)
⇒x³+y³+z³−3xyz=0
⇒x³+y³+z³=3xyz
Hence proved.
We know that x³+y³+z³−3xyz=(x+y+z)(x²+y²+z²−xy−yz−zx)
Given x+y+z=0
x³+y³+z³−3xyz=(0)(x²+y²+z²−xy−yz−zx)
⇒x³+y³+z³−3xyz=0
⇒x³+y³+z³=3xyz
Hence proved.