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AM,GM,HM Inequality

Let a,b,c b...

Question

Let $a, b, c$ be unequal real numbers. If $a, b, c$ are in $G . P$ and $a + b + c = b x$ then $x$ can not be equal to

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Solution

The correct option is D $3$
abc = G.P
$∴ b^{2} = a c$
and $a + b + c = b x$
as $G . M > A M$
and G.M = b
and $A . M = \frac{a + b + c}{3}$ or $\frac{b x}{3}$
$∴ b > \frac{b x}{3}$
$3 b > b x$
or $3 > x$
$∴ x$ can't be equal to $3$
option D is correct.

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