Question

For what value of x are the number x + 9 x minus 6 and 4 in gp

Answer 1

Step-by-step explanation:

the given series is

x+9, x-6, 4

the series to be in GP it should have common ratio

$\frac{t2}{t1} = \frac{t3}{t2} \\ \frac{x - 6}{x + 9} = \frac{4}{x - 6} \\ (x - 6)(x - 6) = 4(x + 9) \\ {x}^{2} - 12x + 36 = 4x + 36 \\ {x}^{2} - 12x + 36 - 4x - 36 = 0 \\ {x}^{2} - 16x = 0 \\ x(x - 16) = 0 \\ x = 0 \: \: \: \: \: x - 16 = 0 \\ x = 0 \: \: \: \: \: \: x = 16$

we get 2 values of x as 0 and 16

verification

if x = 0

x + 9 = 0 + 9 = 9

x - 6 = 0 - 6 = -6

r = -2/3

the GP is 9, -6, 4

if x = 16

x + 9 = 16 + 9 = 25

x - 6 = 16 - 6 = 10

r = 2/5

the GP is 25, 10, 4

hope you get your answer