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Question
For what values of x, the numbers `-2/7, x, -7/2` are in G.P?
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Solution
The given numbers are `(-2)/7, x, (-7)/2`
Common ratio = `x/(-2/7) = (-7x)/(2)`
Also, common ratio = `(-7/2)/(x) = (-7)/(2x)`
∴ `(-7x)/2 = (-7)/(2x)`
= `x^2 = (-2 xx 7)/(-2 xx 7) = 1`
= x = `sqrt1`
= x = ± 1
Thus, for x = ± 1, the given numbers will be in G.P.
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