Question 6

For what values of x, the numbers 2 over 7 comma x comma fraction numerator minus 7 over denominator 2 end fraction spaceare 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

so

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.

Write a Comment: