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प्रश्न
If a, b and c are in A.P. and also in G.P., show that : a = b = c.
उत्तर
a, b and c are in A.P.
`=>` 2b = a + c
`=> b = (a + c)/2`
a, b and c are also in G.P.
`=>` b2 = ac
`=> ((a + c)/2)^2 = ac`
`=> (a^2 + c^2 + 2ac)/4 = ac`
`=>` a2 + c2 + 2ac = 4ac
`=>` a2 + c2 – 2ac = 0
`=>` (a – c)2 = 0
`=>` a – c = 0
`=>` a = c
Now, 2b = a + c
`=>` 2b = a + a
`=>` 2b = 2a
`=>` b = a
Thus, we have a = b = c
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