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Question
If a, b and c are in A.P, a, x, b are in G.P. whereas b, y and c are also in G.P.
Show that : x2, b2, y2 are in A.P.
Solution
a, b and c are in A.P.
`=>` 2b = a + c
a, x and b are in G.P.
`=>` x2 = ab
b, y and c are in G.P.
`=>` y2 = bc
Now,
x2 + y2 = ab + bc
= b(a + c)
= b × 2b
= 2b2
`=>` x2, b2 and y2 are in A.P.
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