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Q.

If $a, b, c$ are three distinct real numbers are in G.P and then $a + b + c = x b$ Which of the following statements are true
Statement-I : $x$ can not take the values between -1 and 2
Statement-II : The least positive integral value of $x$ is 3

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a

I is true, II is false

b

I is false, II is true

c

Both I and II are true

d

Both I and II are false

answer is C.

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Detailed Solution

detailed_solution_thumbnail

$a + a r + a r^{2} = x . a r$

$\Rightarrow x = r + \frac{1}{r} + 1$

$If r > 0 then x > 3$

$r < 0 then x < - 1$

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