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If a,b,c are three distinct positive rea...

If a,b,c are three distinct positive real numbers in G.P., than prove that `c^2+2ab gt 3ac`.

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Since a,b,c are three distinct positive real numbers, so applying `A.M gt G.M` in `c^(2)`, ab,ab we get
`(c^(2) + ab + ab)/(3) gt (c^(2) b^(2) a^(2))^(1//3)`
or `(c^(2) + 2ab)/(3) gt (c^(2) aca^(2))^((1)/(2))` ( `:'` b is G.M of a and c)
or `c^(2) + 2ab gt 3ac`
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