Question

For what value of x, the numbers -2/7, x , -7/2 are in G.P​

Answer 1

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GIVEN :

$\sf {- \frac{2}{7} \: ,x , \: - \frac{7}{2} \: are \: in \: G.P}$

TO FIND :

Value of x

SOLUTION :

Here ,

$\sf{t_{1} = - \frac{2}{7} , \: t_{2}= x, \: t_{3}= - \frac{7}{2} }$

As they are in G.P, they have common ratio.

$\sf{ \therefore \: \frac{ t_{2}}{t_{1}} = \: \frac{ t_{3}}{t_{2}}}$

On putting the values we get,

$\implies \: \frac{ \: \: x \: \: } { \frac{ - 2}{7} } = \frac{ \frac{ \: - 7}{2} \: \: }{x}$

$\sf {\implies \: \frac{ - 7x}{2} = \frac{ - 7}{2x}}$

$\sf {\implies \: {x}^{2} (\frac{ - 7}{2}) = \frac{ - 7}{2}}$

On cancelling we get,

$\implies \: \sf {{x}^{2} = 1}$

$\sf {\implies \: x = 1 \: or \: x = - 1}$

$\boxed{\sf {\therefore \: x = \pm1}}$

Answer 2

Answer:

here's solution ⤴⤴

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