(x-y) (x2 + xy + y2) + (y-2) (y2+yz +z²)+ ( z- x) ( z²+ zx + x²)
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2
Answer:
here
Step-by-step explanation:
It is given that x, y, z are in A.P. Therefore, y−x=z−y=d(say)
Now, (x
2
+zx+z
2
)−(x
2
+xy+y
2
)=(−y
2
+z
2
)+x(z−y)=(z−y)(x+y+z)=d(x+y+z)
and, (z
2
+yz+y
2
)−(z
2
+zx+x
2
)=(y
2
−x
2
)+z(y−x)=(y−x)(x+y+z)=d(x+y+z)
∴(x
2
+zx+z
2
)−(x
2
+xy+y
2
)=(z
2
+yz+y
2
)−(z
2
+zx+x
2
)
⇒x
2
+xy+y
2
,z
2
+zx+x
2
,y
2
+yz+z
2
are in A.P.
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