(x^2/y^2 + y^2/ z^2)(y^2/ z^2 + z^2/x^2)(z^2/x^2+x^2/y^2)
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Answer:
t 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
)=d(x+y+z)
⇒x
2
+xy+y
2
,z
2
+zx+x
2
,y
2
+yz+z
2
are in A.P.
Explanation:
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