Question

(x-y) (x2 + xy + y2) + (y-2) (y2+yz +z²)+ ( z- x) ( z²+ zx + x²)​

Answer 1

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.