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for what values of nbsp x nbsp the numbers nbsp a...

Question:
For what values of x, the numbers $2 over 7 comma x comma fraction numerator minus 7 over denominator 2 end fraction space$ are in G.P?

Answer:

The given numbers are $fraction numerator minus 2 over denominator 7 end fraction comma space x comma space fraction numerator minus 7 over denominator 2 end fraction$ .

Common ratio = $fraction numerator x over denominator begin display style fraction numerator minus 2 over denominator 7 end fraction end style end fraction equals fraction numerator minus 7 x over denominator 2 end fraction$

Also, common ratio = $fraction numerator minus 7 over denominator begin display style 2 over x end style end fraction equals fraction numerator minus 7 over denominator 2 x end fraction$

$fraction numerator minus 7 x over denominator 2 end fraction equals fraction numerator minus 7 over denominator 2 x end fraction rightwards double arrow x squared equals fraction numerator minus 2 space cross times 7 over denominator minus 2 space cross times 7 end fraction space equals 1 rightwards double arrow x space equals space square root of 1 space rightwards double arrow x space equals space plus-or-minus 1 space$

Thus, for x = ± 1, the given numbers will be in G.P.

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Question:
For what values of x, the numbers $2 over 7 comma x comma fraction numerator minus 7 over denominator 2 end fraction space$ are in G.P?

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Question:
For what values of x, the numbers $2 over 7 comma x comma fraction numerator minus 7 over denominator 2 end fraction space$ are in G.P?